Re: workaholic husband
I'm sorry for what you're going through--angry outbursts can be jarring and take their toll.
He is probably feeling the burden of taking care of the whole family--is there any way you could go back to work? I know it's tough finding a job, but it might earn you more respect if you're contributing financially. He doesn't seem to understand that you can contribute in other ways. Maybe you could also try talking to him about how you're shouldering the burden for providing emotionally for the family--damage control with his anger, staying upbeat for the kids, etc. Comparing it to how he contributes financially might help him understand better.
Just a word about the final exam--as tough as it was, I think that your husband made the right decision. I'm not sure if all competitive graduate programs are alike, but in mine it's basically impossible to miss/reschedule finals, even for absolute emergencies. I agree that he was overly harsh in how he communicated his desire to stay and take the final, but I think he made the right decision. He might not have had lenient professors, passed the course, or became a lawyer had he skipped the exam--it sounds extreme, but there is very little hand holding in higher education. A broken down car is a really tough situation, but it looks like you got it resolved on your own. I think the real issue is not that he wasn't there to help, but that he didn't apologize or feel empathetic towards your situation, which can be just as hurtful.