So is the issue that they won’t pay for college AT ALL, or just not outside of Texas? Unless you have the stats for a full ride (tuiton, room and board) at a college, staying in Texas is realistically your only option.
Lots of people really want to go to college in NYC. Be aware that Fordham is not in Manhattan. It’s in a not particularly great area, the Bronx, and you will still have to get into Manhattan from there.
Your plan is not realistic. Go to school in Texas, live away from home if your parents will pay, then move after you graduate.