BEDFORD, Texas — As the Fourth of July weekend begins, families across the country are making summer vacation plans and many will go on a cruise hoping for the trip of a lifetime. For a few, it will be a trip they wish they'd never taken.

Anne Smith was one of those people. The 42-year-old single mother splurged and took her two daughters on a Caribbean cruise.

"We rarely get to go places as a family, so of course an opportunity to get away from the world and be with your girls is a really big deal," said Smith. "It went great at first and you know we had fun, got to see the beaches, we went horseback riding even."

But near the end of the cruise her 16-year-old daughter Abby came to her confused and in tears.

"I think I got molested," Abby told her mother.

The teen says she was sexually assaulted by a trainer in the gym on board the Carnival cruise ship.

"It was my final consultation to see how I had improved and so he took my measurements and he was like lifting my shirt and all that and pulling down my shorts," she said.

"I realized he shouldn't have been doing that, when he extremely touched me in places where he shouldn't have been touching me."

Anne Smith and her daughters Carly and Abby (right) onshore during their cruise. The individual whose face is blurred has no connection to the alleged incident aboard the ship. Courtesy Anne Smith

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Abby and her mother say they immediately reported the alleged incident to staff on board the ship and the cruise line initially tried to help the family.

"They did take a report. They took evidence. They took her underwear and things like that. They called the FBI, so we had them waiting for us when we got back to the port," said Anne.

But once the family got back to land they discovered how difficult these cases can be to pursue. No charges were ever filed.

The Smiths are not alone. Over the course of three months, NBC News spoke with 10 victims of sexual assaults or members of their families. We found that these floating cities can pose a hidden danger.

Of the 92 alleged on-board crimes reported by cruise lines in 2016, 62 were sexual assaults. When sexual assaults occur at sea, it may be hard for victims to get justice on land. Some assaults were barely investigated, according to the victims and families who spoke to NBC. Most were never prosecuted.

And perhaps most troubling, many of the sexual assaults on-board cruise ships involved minors. A congressional report in 2013 found that minors were victims in a third of the assaults.

Abby Smith (left) and her mother Anne. NBC News

"It happens more often than the cruise lines will admit," said Miami attorney Jim Walker, whose firm has represented alleged victims as young as three years old.

Walker says that when sexual assaults occur aboard cruise ships, they are often committed by the staff. Crew members sometimes groom victims, he said, gaining their trust.

"A lot of times the victims will be so confused, so shocked, they'll actually leave the ship without reporting it on the ship. And I think crew members are kind of banking on that possibility," said Walker.

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Whether on land or at sea, sexual assaults are not always reported right away. Victims are often traumatized or embarrassed and don't speak up. That's exactly what happened to one family from the Midwest who asked not to be identified.

Anne Smith and her daughters ride horses during their cruise. Abby is on the left. Courtesy Anne Smith

The family's 15-year-old daughter began acting out after their cruise. According to her mother, she attempted suicide just weeks after the family returned home. Months later, when she got drunk and sick on a camping trip, she told her mother what had happened on the ship.

"She had thrown up. And I went to lift her shirt off, and it was then that she told me 'No!' And then she kind of backed up," said the mom. "And she said, 'No. I told him no, and he raped me.' And that was when I found out. Up until that point [it] never did it cross my mind that something had occurred."

In this family's case, the daughter was allegedly raped by a male she met while on a cruise through the Virgin Islands in March 2016. The daughter and the male went to an area of the ship where alcohol was served, according to the mother, and that's when things took a dark turn.

"I believe she had a cocktail and then she had another cocktail that he got her. And then he asked if she'd like to go to a stateroom or walk down and get something from the room," said the mom. "And he forcefully pushed her down and assaulted her."

The daughter did not tell her mother right away and did not report the incident to the ship. Instead, according to her mother, she started having behavioral issues.

When the daughter finally confided in her mother, a battery of tests were conducted for STDs and her local sheriff's department was contacted. But so far no charges have been filed, leaving the mom feeling guilty.

"I shouldn't have let my motherly instincts guard down," said the mom. "I needed to be treating my children as if we were downtown in a major city at night with a big party going on."

Questions of jurisdiction when an alleged crime occurs aboard a cruise ship can be complicated. The ship may be registered in a non-U.S. country, the incident may occur in international waters, and the alleged perpetrator may be a foreign national.

Florida does have jurisdiction over ships that depart from its ports, and its local law enforcement agencies sometimes handle cases. The U.S. government has jurisdiction when a crime occurs against a U.S. national on a ship that has departed from or will arrive in a U.S. port. In those instances, the FBI may be the investigating agency.

Even when U.S. law enforcement becomes involved immediately, victims can feel let down, as the Smiths discovered after Abby reported an assault.

"I think the biggest disappointment were the actual FBI," said Abby's mother Anne. "They took a brief statement from both of us, and pretty much made it clear that there wasn't gonna be much after that."

Carnival Cruise Line said in a statement that it had followed "all established and required procedures" when Abby reported an assault. "We take great pride and care in providing our guests a safe and secure vacation environment and it is the single most important fundamental to our operations."

Carnival said that it had responded immediately and offered medical attention. The FBI interviewed Abby and the alleged perpetrator the next day in Galveston, Texas, but no charges were filed, said Carnival, because of lack of evidence and conflicting information from the accuser and the accused. According to Carnival, the alleged perpetrator was employed by a third-party contractor working for the cruise line, and is no longer working aboard any Carnival ship.

The cruise line offered "heartfelt apologies" to the Smiths in an email. Carnival also offered the family a refund and a complimentary cruise, and said it would pay for Abby's counseling.

Abby Smith (left), her mother Anne and their dog. NBC News

The FBI said it could not discuss the specifics of Abby's case. In a statement, the bureau said it "remains committed to investigating these crimes and bringing justice for the victims and their families." But the statement also noted that crimes committed aboard ships "pose specific challenges for investigators, who may not have immediate access to the ships and to crime scenes or witnesses. The FBI works closely and tirelessly with our partners in law enforcement and in the cruising industry to mitigate these challenges and collect the evidence and facts of the case in order to make a recommendation to the Department of Justice for prosecution."

In the few cases where the suspect is prosecuted, the outcome still does not always give the victim a sense of justice. That's the case for one family in Canada whose then-14-year-old daughter was assaulted by two 16-year-old fellow passengers while on a cruise off the coast of Florida.

"In our eyes they basically got a slap on the wrist."

According to the police report, the girl was immediately transported to a local crisis center onshore where a rape kit was performed.

Ultimately, the boys received community service, sex offender treatment, several months of court monitoring and a curfew, and were ordered to pay for any counseling the victim required. The victim's family was not satisfied.

"In our eyes they basically got a slap on the wrist," said the mom. "When I found out what the sentencing was I was really upset."

The cruise line industry says it serves more than 24 million passengers a year, and has "robust security" that keeps passengers safe. Michael McGarry, senior vice president for public affairs with the Cruise Lines International Association, a trade group, said that the number of assaults is relatively low in comparison to the millions who take cruises, and a "small fraction of the comparable rates of crime on land."

"We are unaware of any case where a cruise line did not report an alleged serious crime as required by law," said McGarry. "Out of a strong duty of care for guests, cruise lines are motivated to ensure that any allegation of a serious crime is immediately reported. … Cruise lines have every incentive to ensure a safe and enjoyable holiday experience for all passengers and therefore continually assess improvements to passenger security and safety."

Plaintiff's attorneys, victims' advocates and parents we spoke with say cruise ships have the same dangers as any city. There are no police on board. And cruise ships are only required to have their own private security, creating a potential conflict of interest.

"There's not law enforcement on these ships, so when a crime occurs the reporting has to be done to the cruise ship security," said attorney Jim Walker. "There's a conflict of interest, of course, in having the security investigating a crime that involved one of the ship employees."

Additional problems arise when cruise lines have to investigate crimes that involve passengers.

"Part of the problem is as soon as someone gets hurt, as soon as someone gets raped, as soon as something bad happens, [the cruise line is] no longer your friend, they're not there to protect you," said Michael Winkleman, a Miami-based plaintiff's attorney whose firm has sued cruise lines on behalf of more than 100 alleged victims of crimes aboard ships.

"Cruise lines, once you get hurt, they see you as their adversary because, chances are there's going to be a lawsuit that comes afterwards."

Cruise lines are required by law to report alleged crimes that fall into eight categories – one of them being sexual assault.

Lawmakers are trying to strengthen the reporting requirements.

"The dirty secret in the cruise line industry is that crime does occur on cruise ships and very often law enforcement isn't notified, evidence isn't preserved, people aren't assisted," said Sen. Richard Blumenthal, D.-Conn. "Some cruise ships do better than others, but when a crime occurs on a cruise ship in foreign waters, often the victim is dependent on local law enforcement."

Blumenthal recently introduced legislation that would require cruise lines to notify the FBI within four hours of a crime and turn over video evidence, identify which alleged crimes were committed against minors, and require that federal officers known as sea marshals be on all ships.

"Look at it this way," he said. "A cruise ship is like a small town and it has all of the responsibilities of a small town, but very often fails to fulfill that kind of trust."

Many of the alleged victims and their families say that trust has been lost.

"People of authority, I automatically try to avoid them," said Abby Smith. "And I don't trust them because in the back of my mind I think, 'What if they're going to take advantage of me?'"

Many of the young women NBC News spoke to are now in counseling. All the families of the alleged victims we spoke to are suing or plan to sue, most because they say they believe that's their best hope of justice, and for holding the cruise lines accountable.

"We're hoping that we can save another family from having to go through this hardship," said one mother. "We don't want another individual to be assaulted on a cruise ship."