And another ‘it depends.’ Some states might start your residency when your father moves, so it might be best to have him move officially (for tax purposes) as of July 1 or Aug 1. That might be easy to do if he gets a driver’s license, changes the state that taxes him on his paycheck, get all the utilities set up at a new place, make sure he uses everything as a local. Buy a fishing license, get a library card, register his car. Some people put those things off for a few months but in your case you may not want to delay anything.
If you tell us the states, we might be able to help more. For example, in Colorado either parent can be the state resident. Florida may be that way too and documentation of the ‘little things’ is important because they don’t have a state income tax filing requirement.
If you want to go to college in your current state, then stall stall stall!