Moriah Barnhart's daughter, Dahlia, was diagnosed with brain cancer at age 2. Moriah said that Dahlia, now 4, was not expected by doctors to live as long as she has.

But the blue-eyed, rambunctious little girl has exceeded doctors' expectations.

"The majority of the progress I've seen in her, physically, mentally and emotionally" is due to cannabis, Barnhart told CNBC. Moriah is one of four mothers who refer to themselves as the Cannamoms, advocating for medical marijuana to be legalized in all states so that their critically ill children, and others like them, can have access to a drug that is still illegal on the federal level. Read MoreThe hottest pot store in San Francisco Throughout her chemotherapy and beyond, Moriah said cannabis had helped Dahlia tremendously, but she can't get access to marijuana legally in Florida, where she lives. Moriah and three other mothers made the journey from Florida to California to try cannabis for a protracted stay. All four at some point have given their children marijuana, and they say they witnessed an improvement in their well being afterward. A few organizations, such as MedMen, the nonprofit Cann-I-Dream, and the medical marijuana dispensary Harborside Health Center, helped fund their visits and doctors' appointments of the parents who spoke to CNBC.



A self-proclaimed "Cannamom" shows some of the medical cannabis she procured for her child. Dina Gusovsky | CNBC

They're not alone. The Cannamoms are part of just a handful of the hundreds of families from across the country who have relocated or are considering moving to a state where medical marijuana is legal. "What we need to focus on is the unlawful laws that make us relocate or move to states that already have cannabis legally for medicinal purposes," Cannamom Renee Petro, whose son Branden suffers from intractable seizures, told CNBC. Read MoreColorado pot demand 'much greater' than expected Since the visit in mid-October, at least two of the mothers have decided to move to California.



Steve DeAngelo, co-founder of Harborside Health Center, argued that families should not have to uproot their lives in order to get access to cannabis.

"There's a lot of ways that a legal cannabis industry can bring financial and fiscal benefits to communities," DeAngelo told CNBC. "I hope that one of them isn't the continued migration of patients and parents from other states to California. I think that that's really a terrible way to build an industry." Medical marijuana has brought in billions of dollars to states that have legalized it, and those numbers are likely to increase in the years to come if and when more states legalize. Read MoreSlideshow: The booming business of cannabis But medical cannabis is not cheap. A regular consultation with California-based cannabis expert and family physician Dr. Frank Lucido costs up to $600 including a few follow-ups. But not everyone agrees that marijuana should be considered as an option to treat some illnesses, especially in children.

"The negative side effects are basically anxiety, paranoia, potential psychosis, memory impairment, visual coordination impairment," Child and Adolescent Psychiatrist Dr. Ankur Desai told CNBC. "You have to think about the benefits and the risks. And at this point, it's about the benefits outweighing the risks, and I don't think we are there yet in terms of the empirical research and support."