How do I change legal custody of my daughter?

My daughter’s father and I have shared legal custody. I am Iranian and practice Islam, he is from the U.S. and is a devout catholic. Our religious differences are part of the reason the marriage failed. When my daughter was born I agreed she could be raised Catholic. She is 15 now and wants to convert to Islam and wants to join my mosque. Her father is adamantly opposed to this and says he will take me to court and sue for full custody of her if I allow her to practice Islam or attend mosque. How do I change the custody order so that I have legal custody and the authority to let me daughter change her religion? Is she old enough that her wishes will be considered? Is the fact that she is 15 and is making her own decision to convert to Islam enough to change legal custody?