This is the first part of a series on health care refugees. Read the second part here .

(CNN) Kim and Richard Muszynski love Florida. They love the beaches and the fishing and the beautiful weather and the Sunday afternoon barbecues with their large extended family.

Rich has lived in Florida all his life and Kim since she was 6 years old.

But in September, the couple left the Sunshine State. They packed their bags, took their 5-year-old daughter, Abby, and moved away.

They wept as they kissed their older daughters, Katlin, 22, and Christina, 16, goodbye, leaving Christina to finish the last half of high school without them. They wept again as they said goodbye to their parents and friends and Rich's job on a fishing boat and the only community they've ever known.

The Muszynskis say they fled Florida because they think Abby's health insurance was killing her.

Abby was born missing a piece of her brain and while in Florida had frequent, large seizures, sometimes several in one day, that shook her entire body. She gasped for air, and her parents gave her oxygen and prayed she'd keep breathing, but doctors warned them that any seizure at any time could mean the end of her life.

Like nearly half of all children in Florida , Abby has Medicaid, the state-run health insurance. Her parents say that instead of being helpful, Florida Medicaid refused to pay for lifesaving medicines and took so long to pay some of her health care providers that at times, they refused to treat her.

Advocates for children on Medicaid say that the Muszynskis' story doesn't surprise them and that they see families leaving a handful of other states too in search of better Medicaid programs.

"The state has done everything in its power to support this family," Mallory McManus, communications director for Florida's Agency for Health Care Administration, the agency that administers the state's Medicaid program, wrote in an email. "Our number one priority has always been -- and remains -- insuring health care services are available to all Floridians, especially children."

This doesn't ring true for the Muszynskis or for some other Florida families with Medicaid.

Like Abby, 3-year-old Sofia Patriarca has severe epilepsy and probably will never walk, talk or even sit up by herself. Her parents recently sold their family pizzeria in Lantana and are preparing to leave Florida in December.

"Medicaid forces us to give our children subpar care," said Sofia's mother, Stefany Garcia-Patriarca.

"They treat them like animals instead of children," she said.

A 6-pound, 14-ounce bundle of joy

Kim Lutz and Richard Muszynski (pronounced mew-ZIN-ski) met at a party in the Florida Keys that neither of them really wanted to attend.

It was a few weeks before Christmas in 2004, and Kim's friends invited her to drive down to Islamorada, at the southern tip of the Keys. The party, they promised, would be epic.

But Kim wasn't feeling up for fun. Recently divorced, she was a single mother to Christina, then 5, and working full-time as a paralegal at a large multinational law firm.

He friends begged Kim to come, telling her she needed a break.

Kim finally agreed, and her friend Susie Little spotted Rich singing in the band. She thought he looked like Kim's type -- so clean-cut -- and she introduced them.

Kim asked him to play her favorite song, "Sweet Home Alabama." He did, and later Rich bought her a drink and put his arm around her shoulder and pretended to be her boyfriend when a large lecherous drunk man got a little too close. Later, he told Kim he'd only come to the party because his friend in the band had lost his voice.

Two years later, on the exact same date at the exact same hotel in Islamorada, Kim and Rich were married. Christina, then 7, and Katlin, Rich's 12-year-old daughter from a previous marriage, were the flower girls.

They moved into Kim's townhouse in Boynton Beach on Florida's east coast, about an hour north of Miami, They decided to grow their family, and Kim became pregnant a few years later.

Everything was going well until a little more than halfway through the pregnancy, when a routine ultrasound showed that something might not be right with the baby's brain.

A followup MRI showed that the baby's brain was fine. Kim and Rich breathed a huge sigh or relief, and the rest of her pregnancy proceeded uneventfully.

When Abagayle Rose Muszynski was born September 14, 2011, she was a 6-pound, 14-ounce bundle of joy.

But her left eye wouldn't open.

Abagayle Rose Muszynski was born September 14, 2011, a 6-pound, 14-ounce bundle of joy.

Don't worry, the doctors told Kim and Rich. It's probably just a blocked tear duct. He referred them to a pediatric ophthalmologist.

"I thought, 'OK, this is going to be fine,' " Kim remembers.

To this day, one of Kim's worst memories is watching the ophthalmologist pry open her 5-day-old daughter's eyelid with a metal instrument. Behind the lid, he found an abnormally small eyeball, a condition called microphthalmia.

He told the Muszynskis that Abby would always be blind in that eye, but she could get a prosthetic eyeball and live a normal life. She seemed otherwise healthy -- but he arranged an MRI of Abby's brain just to make sure.

Once again, Kim thought, "OK, this will be fine."

When the doctor called to give the results of the MRI, the Muszynskis instantly knew something was wrong, because he requested that both Kim and Rich come to his office and that they put their pediatrician on speakerphone.

Rich and Kim Muszynski were sad to leave their home state.

They were completely unprepared, however, for just how bad it would be.

The doctor told them the MRI had found that Abby was missing a big chunk of her brain, a piece called the corpus callosum that connects the right and left hemispheres. She also had several other congenital brain defects and microcephaly, a small head.

That's when the Muszynskis learned that their daughter would probably never walk or talk. She would have frequent seizures and would always need a diaper. In addition to the brain defects, she would later be diagnosed with scoliosis and cerebral palsy.

The reason for all these problems was Aicardi syndrome , a rare genetic disorder that affects about 1,000 people in the United States, almost exclusively females. There is no cure.

Doctors have told the Muszynskis that their daughter probably won't live past her 20th birthday.

"I was shattered," said Kim. "She was our dream baby. We were married and happy and financially OK. Our nursery was decorated perfectly. I would just sit and rock her and try to embrace the joy of our new baby, but I was so overwhelmed with sadness and hopelessness."

A neurologist gave Kim and Rich instructions for what to do when she had her first seizure. The couple watched YouTube videos of babies having seizures to prepare for their own baby's first time.

When it happened, it was still terrifying.

A Christmas Day seizure

In a burgundy dress trimmed with white lace, black patent-leather shoes and a matching hair bow, Abby Muszynski celebrated her first Christmas with her parents, older sisters, aunts, uncles and cousins in Boca Raton, Florida.

Kim Muszynski with daughters Christina and Abby.

As the family was opening gifts, Abby had her first seizure. She was 3 months old.

Her arms and legs jerked up and down. Her whole upper body bowed forward, as if she were doing a sit-up.

"Looking back, I think I'd been in denial, that she wouldn't really have seizures, or maybe they would be just mild," said Kim, who was changing Abby's diaper when it happened. "So I was terrified."

Kim yelled for Rich, who scooped up his daughter and headed for the hospital, as the neurologist had instructed. She was later sent by helicopter to Nicklaus Children's Hospital in Miami.

"That was the worst night of my life, to watch my baby be airlifted like that," Kim remembers. "When we got to Miami, I climbed into the crib with her."

Once out of the hospital, Abby started taking an anti-seizure drug and went into day care while Kim returned to her job at the law firm.

But when the medicine didn't work, the center said it couldn't keep her.

"We looked into hiring a full-time nurse for her, but it just wasn't financially feasible," Kim said. "So I resigned a job I loved. I ended my career."

That's when the Muszynski family ended up on Florida Medicaid.

Florida a 'troubled situation'

When Kim quit her job -- and the health insurance that came with it -- in spring 2012, they tried to put Abby on Rich's insurance policy at his work. Inspired by his wife, he'd become a paralegal and was working at a small law firm.

But the Muszynskis said it was prohibitively expensive to add Abby to Rich's policy.

Their income was low enough to qualify for Medicaid. They had no way of knowing that they were joining a system that in the next few years would be harshly reprimanded by judges and the federal government for failing to provide adequate services to sick children like their daughter.

In 2013, a federal judge chastised Florida Medicaid (PDF) for refusing to pay for a therapy called applied behavior analysis. The state's defense was that the therapy was experimental, even though it was considered standard treatment for autism by eight leading health agencies and organizations, including the American Academy of Pediatrics, the National Institute for Neurological Disorders and Stroke and the US Centers for Disease Control and Prevention.

Abby Muszynski was born missing a piece of her brain called the corpus callosum that connects the right and left hemispheres.

McManus, the spokeswoman for Florida's Agency for Health Care Administration, said in response to an inquiry from CNN that "we have recently received approval from (the federal Center for Medicare and Medicaid Services) to expand coverage of behavioral analysis services for any Medicaid eligible child for whom this service is medically necessary."

Then in 2014, the federal Center for Medicare and Medicaid Services threatened to cut millions of dollars in funding to Florida because the state was limiting children on Medicaid to six emergency room visits a year, in violation of federal law.

In 2015, another federal judge ruled that Florida had violated the law by underpaying doctors. The state later reached a settlement (PDF) with the Florida chapter of the American Academy of Pediatrics, the plaintiffs in the case.

Later that year, a Florida judge (PDF) said the state had illegally removed thousands of children from an insurance program for children with special medical needs.

Jane Perkins, legal director of the National Health Law Program, noted that this number of legal decisions against a state in just a few years is unusual and that the letter from the Center for Medicare and Medicaid Services threatening to withhold funds is unusual, too.

"Florida fits in that group of states that's needed courts and the federal government to tell them how Medicaid works," Perkins said.

"Florida is certainly a troubled situation. There's no question," added Joan Alker, executive director of the Center for Children and Families at Georgetown University, who's studied Florida Medicaid for more than a decade.

When asked about the issues that arose in previous years, McManus, the spokeswoman for Florida's Agency for Health Care Administration, pointed out that in 2013 and 2014, Medicaid in the state was transitioning to a managed care system. Such a system is defined by the US National Library of Medicine as a health insurance plan that has contracts with health care providers and medical facilities to provide care for members at reduced costs.

"This transition has allowed our Agency to hold health plans more accountable and focus our efforts on better quality of care, enhanced access requirements and working as partners with advocacy groups who share our goal of better health care for all Floridians," McManus wrote in a statement.

"The cases you cite against the Agency all arose prior to the design and implementation of our new program," she added. "Florida's Medicaid program is currently operating at the highest level of quality in its history."

Almost losing Abby

About the same time judges were reprimanding Florida, the Muszynskis started to experience their own Medicaid struggles.

The couple says that when Abby was 18 months old, her pediatrician requested that Florida Medicaid pay for a wheelchair for her, but it refused.

Kim Muszynski with her daughter Abby.

"I couldn't believe they wouldn't give her something as simple as a wheelchair, given her diagnosis," Kim said.

Kim appealed the denial, and about six months later, Medicaid did pay for it.

Then it got worse.

About the same time her wheelchair was denied, Abby was hospitalized with pneumonia. Respiratory failure is one of the leading causes of death for people with Aicardi syndrome, as they're often too weak to cough properly, and mucus and secretions can get stuck in their airways.

When Abby got out of the hospital, her doctor prescribed respiratory therapy four days a week. After every session, Abby breathed easier -- and her parents did, too.

At the end of one session, the therapist packed up and turned to Kim. He said he would have to stop seeing Abby because Medicaid hadn't paid him for about six weeks. He said he felt terrible, but his agency had rules.

"We were so fearful of losing her," Kim said.

Kim says she pleaded with Medicaid to pay the therapist but said they got nowhere. After several missed sessions, the Muszynskis could see that Abby's breathing was suffering. They paid the therapist $900, and he agreed to see her again.

Kim says that at various other points, Abby's feeding, occupational and physical therapists also stopped seeing her because Medicaid hadn't paid them. Eventually, the therapists were paid, and they resumed caring for her.

According to Kim, Florida Medicaid also initially refused to pay for most of the medications Abby was prescribed to prevent seizures, even though her doctors were adamant she needed those particular drugs.

"I was fighting them constantly, appealing their decisions, writing emails, arguing with them," Kim said.

Using the skills she'd learned in her legal training, Kim says, she eventually prevailed, and Medicaid paid for the drugs.

The medication Diastat helps stop Abby Muszynski's seizures.

There was one medicine, however, that she couldn't get Medicaid to budge on, no matter how many hours she spent calling and emailing and arguing. It was Diastat, a drug that can stop a seizure before it kills her.

Kim says Medicaid would pay for only four doses of Diastat a month, even though Abby was having about eight to 12 large, or grand mal, seizures a month.

She said the family couldn't afford to pay for more doses out of their own pocket: It costs about $250 a dose, and in early 2014, when Abby was 2, Rich was laid off from his job.

Kim says that about once or twice a week for nearly three years, whenever Abby had a seizure and they'd run out of Diastat, they'd call the paramedics and wait until they arrived to give Abby a dose of the drug.

The paramedics were there so often, Kim and Rich gave them their garage door code.

The Muszynskis panicked every time they called the paramedics, praying that Abby would keep breathing until they arrived. They also wondered about the finances of it all. Was Florida really saving money by denying Abby the Diastat? The dose cost $250, but didn't the paramedics cost more, especially as they insisted on transporting Abby to the hospital for observation?

They wondered -- how much did those ambulance runs and hospital stays cost Florida taxpayers?

Fighting to get what they need to survive

The Patriarca family has wondered the same thing.

Up until recently, Christian Patriarca ran the family pizzeria in Lantana, not far from the Muszynskis on Florida's east coast. His wife, Stefany Garcia-Patriarca, left her job as a hotel clerk to care for their 3-year-old daughter, Sofia, who has severe epilepsy and can't walk or talk or even sit up.

She said that as with Abby, Medicaid doesn't pay for enough doses of Diastat for Sofia, and so they often have to call paramedics when they run out. Instead of paying for a $250 dose of Diastat, taxpayers pay for the paramedics to arrive and take Sofia to not one but two hospitals, as she needs to be stabilized at the closest hospital, which doesn't have neurology services, and then taken to a second hospital farther away, which does.

Sofia Patriarca has severe epilepsy and can't walk or talk or even sit up.

Garcia-Patriarca also said that for regularly scheduled appointments with Sofia's neurologist at a Medicaid clinic, they used to wait for four hours in a small room crammed with about a dozen other children and their families. When the children made noise, it sometimes triggered Sofia to have more seizures.

After parents complained about the wait, she said, the clinic was moved to an office with a more spacious waiting room and only two-hour waits. But that office couldn't do simple procedures like taking blood, so she'd have to take Sofia to a lab or the hospital.

The extra trip was a strain on Sofia, who's medically fragile, and her family questioned the financial wisdom of a separate visit for something as simple as a blood draw.

The Patriarcas, who also have a 9-year-old daughter and 4-year-old son, plan to leave Florida in December.

"We decided we just couldn't wait any longer," she said.

Heather Rosenberg said she and her husband have also thought about leaving Florida, but they both work for the state.

The Rosenbergs have extensive experience with Florida Medicaid: They've been foster parents to 16 children and adopted three of them. All of the children have been on Medicaid.

She describes Florida Medicaid as "horrible."

Heather Rosenberg with her sons Liam and Warren. Their mothers were substance abusers, and the children suffer from developmental delays.

"It's an absolute nightmare," she said, adding that she speaks as a mother, not in her role as children's ombudsman at the Florida Department of Children and Families.

Rosenberg describes many of the same problems as the other mothers, such as hours spent on the phone trying to reach someone at Medicaid to fix problems. For example, for just one issue, she had to make about seven phone calls and spend about three hours on hold.

As with Abby, physical therapists and other therapists temporarily stopped seeing two of the Rosenbergs' children because Medicaid paid them late.. As the children missed appointments, their parents could see their development suffer.

She said Medicaid also refused to pay for drugs prescribed by her children's doctors, but she persevered and got the decision reversed.

Janice Mauro said she and her family have constantly had to fight to get her grandchildren, Charlotte and Michael Wolf, what they need.

Both children, ages 4 and 2, have a neurological condition. They can't breathe on their own and are on ventilators. They'll never walk or talk or sit up and are fed by tubes that go into their stomachs.

Michael Wolf and his sister have a neurological condition. They can't breathe on their own and are on ventilators.

She said Medicaid has repeatedly given her family a hard time about paying for certain drugs and medical equipment. Charlotte and Michael's parents have talked about moving out of state, but they don't have family anywhere else to help with the children, who each need around-the-clock care.

"It seems like any way (Medicaid) can get out of giving us something, they do it," she said. "We don't understand why we have to fight so hard for these babies to get what they need to survive."

Charlotte Wolf and her brother will never walk or talk or sit up and are fed by tubes that go into their stomachs.

Children like Abby, Sofia, Charlotte and Michael are, in federal government parlance, "super-utilizers": the 5% of Medicaid beneficiaries who account for 54% of total Medicaid expenditures, according to the federal Center for Medicare and Medicaid Services.

"The bottom line is, these are high-cost cases, and that's where you see efforts to contain costs, and that can cause problems for kids," said Alker, the Medicaid expert at Georgetown.

Speaking generally, "All Medicaid-eligible children are receiving medically necessary services," McManus, the spokeswoman for Florida's Agency for Health Care Administration, wrote in a statement.

"If anyone is aware of a child who is not receiving medically necessary care, they need to contact AHCA immediately. Our Agency works with recipients and guardians every day to ensure that all necessary medical services are being provided."

Abby's 'knight in shining armor'

In February, the Muszynskis received the shocking news that Abby was getting kicked off Medicaid. After rounds of emails and phone calls, Kim said, it still wasn't clear why.

The Muszynskis decided that after years of fighting Florida Medicaid, they needed help, and they found their "knight in shining armor" in Ben Durgan, an aide to state Sen. Joseph Abruzzo.

Kim said Durgan worked nights and weekends to get Abby back on Medicaid, going all the way up to Gov. Rick Scott's office. After about a month, he succeeded, and Abby was put back on the insurance.

Kim says it probably didn't hurt that she and Abby had recently appeared in a local TV news piece about problems with Medicaid.

The Muszynskis soon received an email from an aide to Elizabeth Dudek, the head of Florida's Agency for Health Care Administration, saying Scott's office had asked Dudek to get on the phone with the Muszynskis.

On June 14, the Muszynskis spent an hour on the phone with Dudek, her chief of staff, Toby Philpot, and Justin Senior, the state's deputy secretary of Medicaid, who a few months later would become the agency's interim director when Dudek retired.

The couple told the officials everything: about the therapists who weren't paid and the medicines the family had to fight for and especially about how they didn't have enough Diastat to stop Abby's seizures.

Kim says the officials told them they never should have been denied the doses of Diastat. They promised to investigate all the complaints.

That's why the Muszynskis were incredulous about what happened just a few weeks later.

Abby's neurologist ordered a 24-hour observation at Nicklaus Children's Hospital to figure out why her seizures were getting so much worse. Instead of having two grand mal seizures a week, she was having two a day.

Kim says Medicaid rejected the neurologist's request, saying it would pay for only a one-hour observation.

Abby's neurologist fought back, and Medicaid agreed to pay for the full 24 hours.

That fight might have saved Abby's life. Kim says that about 20 hours into the observation, Abby stopped breathing. Her face and extremities turned blue. Her nurse called a code, and a team rushed in to pump her with oxygen and give her CPR.

"I was sobbing. I thought we'd lost her," Kim remembers.

Abby Muszynski at Nicklaus Children's Hospital.

Abby survived and was discharged from the hospital with a prescription for a higher dose of Diastat, the medicine that stops her seizures.

But when Rich went to the pharmacy that night to fill her prescription, the pharmacist said he couldn't give him the medicine because Abby had been kicked off Medicaid -- again.

Rich called Kim at home. They couldn't believe this was happening again.

Kim, by her own description, went ballistic. She called Abby's case manager at

Medicaid and asked why it had cut off her daughter's insurance when she'd just nearly died. She threatened to sue the state.

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Within a few days, Abby was put back on Medicaid. Kim said her case manager apologized, explaining that Abby was kicked off of Medicaid because of a computer glitch.

For months, Kim and Rich had been going back and forth on whether they should leave Florida.

"After she coded, I said, 'that's it.' I said, 'I'm done with Florida,' " Kim remembers.

It meant leaving a lifetime behind them, but the Muszynskis needed a place where their daughter could get the medical care she needed.

They knew where they would go: Colorado, for better Medicaid and medical marijuana.