According to Florida Statutes, if you don't have his permission to relocate with your children, you must petition the court for permission. If he is as uninvolved as you say he is, it might be worth a try to just ask him for his consent, instead of going to court at all. Otherwise there are Supreme Court approved forms for this process, which can be found on their site www.flcourts.org. Look at forms 12.950 A-J. Read the instructions that go along with the forms, and you'll get a good idea of what to do.
We are not attorneys and do not provide legal advice.