Inside the room where the boys were, authorities found narcotics and weapons.
"They were talking about 'completing their ultimate journey' and were traveling across the country to 'take a journey to the Armageddon,'" police said about the parents.
Louisiana authorities took the children from their parents after that incident.
About two weeks later, the father showed up at a foster family home with a gun and demanded the return of the boys, Slidell police said. He fled after the foster parents called 911.
Over subsequent months, the parents "did not participate in the system," said Sheriff David Gee of Hillsborough County. He did not offer details.
"As a result of that, the authorities in Louisiana gave custody to the grandparents," he said.
That transfer became official on April 2, when a Louisiana judge terminated the suspects' parental rights.
Early the next morning, Patricia Hauser told police, Josh Hakken entered her Florida home, tied her up and sped away with the children and the family dog in a silver 2009 Toyota Camry.
They met up with Sharyn Hakken, sheriff's investigators said, and eventually ended up on a 25-foot sailboat named Salty.
The boat's seller later tipped off authorities after word got out about the alleged abduction.
It was at the Hemingway Marina just west of Havana, on Tuesday, that CNN found the family -- hunkered inside the boat, under the watch of Cuban security forces.
That morning, U.S. officials in Havana told CNN that they were afraid the children could be in danger from their parents.
Armed Cuban security agents watched over the family most of the day until the parents and children were led away peacefully that afternoon.
Boys 'fine, happy and sleepy' on return to U.S.
Cuba and the United States are divided by far more than the Straits of Florida. But this week, U.S. officials repeatedly expressed their appreciation for the Cuban government's "extensive cooperation."
The Cuban Foreign Ministry said the boat pulled into the marina in bad weather Sunday.
The two governments shared information, which led to the return of the family and their dog to the United States.