I see red flags everywhere in your post, Amy. I'll admit I may be oversensitive to the combo of infidelity, alcholol, physical violence, and Jekyll/Hyde personalities. However, before your situation improves, I see people taking a big risk of getting seriously hurt. You can't reason with alcohol. It's a mugs game. Trust me on that. I found out the hard way. Alcohol is a bitch goddess. Tough to compete with a mistress like that.
Has your H ever shoved, pushed, or slapped you, Amy? You don't have to answer that, of course. I'm just raising the issue.
I hope you get to talk to some people who know something about life with a "heavy drinker". It's not something that a person can deal with alone.