Is there some place where you could store the car that is away from your house? I can understand the temptation to want to work on it if it is sitting right there in the garage staring at you every day. I think if you could put it away and out of mind for a few months it would help. I agree that a car is just metal and relationships are much more important, but you wouldn't want selling the car that is so important to you to become a bitter point in your relationship. My wife and I had a similar discussion reguarding softball last summer. This year I gave up some tournaments, and my work league, but I do still play once a week.
It sounds to me like a compromise can be found. Maybe a set schedule of how much time a week can be spent on the car?
In the end I think you are just going to have to go with your heart, I know it is a tough decision to find.
Final thought...Time is the one thing that we all have in common, and the one thing that we can never get back once it is spent.