"He'll have to face in Hillsborough county the charges he has with the sheriff's office," spokeswoman Cristal Bermudez Nunez Nunez said. She said she did not know how the family would be returned or what will happen when they arrive on U.S. soil.
Terri Durdaller, a spokeswoman at the Florida Department of Children and Families, said it was not clear where the children will ultimately be placed.
"Louisiana is the ultimate decision maker on where these children will reside. It's likely they will be placed back in Florida with the grandmother," she said.
The family's flight to Cuba harkened back to the 1999 child custody case involving Elian Gonzalez, though unlike Gonzalez, the Hakkens had no apparent ties to the island.
In 1999, 5-year-old Gonzalez was found clinging to an inner tube off Florida after his mother and others drowned while fleeing Cuba toward American soil. The boy was taken to Miami to live with relatives, but his father in Cuba demanded the boy be sent back.
U.S. courts ultimately ruled Gonzalez should be sent back, though his Miami relatives refused to return him. In April 2000, U.S. federal agents raided the family's home and he was returned to Cuba soon after. He has since grown into a young man and joined a military academy.
At the Havana marina on Tuesday, the family showed no sign they knew a decision about their fate had been made. The four strolled by an outdoor restaurant as security officials kept reporters at a distance. The youngest child was seated in a stroller and the elder boy sat down on a curb.