You were legally dad's tax dependent on 12/31/2018.
if he chose not to claim you, that doesn't change that you were legally dad's tax dependent on 12/31/2018.
Nor do you qualify for in-state tuition in NY. One of the requirements to be an in-state student is
One does not acquire a new domicile simply by a presence in New York State for attendance at an institution of higher education.
** This is exactly what you are trying to do and it does not qualify you for NY in-state tuition rates.
If dad wants to take the tax dependent for you, he should file an amended tax return.
If he wants to give it to your mom, that's his decision.
On a side note, almost all states do not allow in-state tuition for incoming freshman directly out of high school unless they graduated from a high school in the state or one of their parents is currently paying residential taxes in that state.
- The exception to that you have to prove that you paid for ALL OF YOUR EXPENSES for a year - that you didn't get any money from someone out of state and that no one out of state paid for any of your bills (car insurance, health insurance, cell phone, etc). When you can show this for a year before starting school, then you can prove that you did not move to the area solely for in-state tuition. If you have already started school as an out of state student, you will remain an out of state student until the completion of your program (ie, bachelors degree).
The "but I got a drivers license in the new state" makes you a resident of the state, it does not make you eligible for in-state tuition rates.