The problem isn't that there's something wrong with you. The problem is you're trying to have a relationship with an abusive, controlling alcoholic. A relationship with an abusive alcoholic is he11. I know, my parents had a relationship like that.
"I've been holding on with a death grip, believing divorce is wrong and bad for my kids. "
As one who grew up in an environment similar to that of your kids--my father was the abusive alcoholic who abused my mother and his kids--you are doing them no favor to stay in this relationship. As some have already said, the kids are learning that this is what a relationship is like. Is this what you want for your kids?