My 16 year old daughter wants to move with me permantley but I don't want to take custody from her mom I just want to be able to live with me and not worry that her mom will try to hurt her for choosing to live with me! Does anyone have any ideas about the state of Florida laws about this subject?

Yes, she will live with her mother unless her mother says she can go.

You can file in court for custody and if the 16 tells the court she wants to live withyou, then they should let her unless there is a reason not to.

So if you want her to, you file in court for her to live with you, or tell the 16 that you don't want to go to court to make it happen.