Since you are already staying at his place for half a week, he must be living closely enough. So you would not be moving to another state, and would still be able to visit your parents regularly and to help your dad get through life with his illness. Have you considered that it is not a major move?

I think the main problem is that you are trying to feel differently from what you feel, "like everyone else". If you stop trying and just feel your current feelings through and through, you might be surprised when you find relief and even, possibly, joy, but trying to tell yourself how to feel would only frustrate and possibly even shame you. What is th point in doing that?