I am sorry to say this, but I think that unless your H gets help for his alcoholism this is no possibility that you can work anything out with him. His mood swings and temper tantrums are typical of the alcoholic. I know, I am the mother of one. I have lived with the kind of behavior you describe and it is awful. Like living on the flanks of a volcano, always expecting an eruption. The best thing that ever happened to my son was that he was arrested and put in a rehab program and forced to take a drug called antabuse that prevented him from drinking. (The night he put the drug to the test was really frightening. He never did that again.) They turned my son back into a person.
At this point your H is totally out of control. I suspect the affair is more a symptom of his drinking problem than it is a stand alone problem. I can't offer advice except to hope that he does get arrested for drunk driving.