Once your over a certain age and maturity most courts will allow the child to decide. If you are in your teens you sould be able to live with which ever parent you like. If your dad has the money (which he may not living in an expensive area like NY) he could take your mom to family court I suppose. You would tell the judge you want to live with your dad. Most courts won't tell the kid no unless something comes out that may suggest your dad isn't fit to raise you.

Other than that, if your mom won't let you go, I'm not sure what to suggest. It also sounds like it depends if there is shared custody or if your mom has full custody.

When I was about 14 I told my mom I wanted to live with my dad. She broke down crying so I figured I would just deal for the next few years. It wasn't worth breaking her heart over it.