
Quoting
Dogmatique
You must follow the law.
You're correct - your ideas on Dad's parenting are completely irrelevant in court. He's allowed to let them stay up and play video games if he wishes.
Florida is actually one of the more progressive states when it comes to Father's Rights. It's a myth that most judges favor the female parent. Ownership of the uterus does not make a whit of difference these days (and rightly so).
You haven't indicated, however, why the move would be in the best interest of the child/ren. You may have to make a decision - relocate without the child, or stay put.