Florida passed laws to spell out what is required before you can move a child after divorce. Known as the "Child Relocation Law," Florida Statute 61.13001 requires that the non-moving parent agree to a relocation or the parent who wants to move must file a petition and ask the court for permission to move when the move is more than 50 miles. Even when there is a agreement, the law requires it be written and approved by the court. So, the short answer is no, he can't just move away and take the children.
The Florida Child Relocation Law applies to all Florida divorce judgments unless there is another relocation provision in your final judgment. The Florida divorce laws also prohibit a move, unless there is an agreement or court order, once the divorce case is filed with the court. So as long as there is a final judgment, temporary order or the divorce case has been filed with the court, she can't just move and take the kids.