It sounds to me as if you resent your stepfather so much that he can't do anything right. I think the suggestion of the hotel is a good one, really, since you obviously are not comfortable staying in his house.

Of course, you could just get the dog groomed and that would take care of the problem for now (and with the heat, the dog would feel better, yes?).

I think he's (your stepfather's) a bit overbearing and you're right to be feeling uncomfortable.