Attempts to relocate out of Florida are being denied by Florida judges pretty much daily. Very rarely is a parent allowed to take the kids away from the other parent. His odds aren't good. On the other hand, if he wants to relocate and leave you the kids, that's his business; he can do that if he wants. If he does, child support will be calculated according to Florida's guidelines system, and neither of you can legally control that.
In terms of you changing custody based on him "bribing" you, I think you can forget it. He's not bribing you, he's just trying to work a deal. That's his right. Changing a custody deal after it's made is a very difficult thing to do (like moving the kids away is a difficult thing to do). Once a deal is made in a divorce case, it's tough to change it unless both sides agree. To change a custody agreement, one of you has to prove a substantial, unexpected change of circumstances affecting the kids. "Bribery" doesn't cut it. His moving away without the kids would cut it, but he hasn't done that yet. And his moving away with the kids probably isn't going to happen.
