My mother wont let me and my father move to New York?

So ive lived with my dad basically my whole life, an me an my mother got into a huge fight when i was 12 an haven't talked to her up until recently (im now 16). All of my father's side of the family lives up in new york an that's where ive wanted to be sense we moved down here (to florida) an my father and i just started talking about moving to new york an the only thing he said that's holding us back is that he doesn't want my mother to take him to court and not let me go to new york with him. so me and him came up with this agreement that if my mother signs this legal document that says that she will let me move to NY with him, that we will go. the only problem is she said shes not going to sign it and wont let me go. is there any way i could convince her to let me go or if we do go to court the judge would let me go with my father right ? please help