Your affair is not a reason to drink, its an excuse to drink. So now you know, Rehab didn't work.
As for your affair, you were checked out of the marriage. I applaud you for telling her when you decided to try to keep the marriage intact, but I am also sympathetic to her as its a hard pill to swallow. Her alcoholism did not MAKE you sleep with someone else just like your sleeping with someone else did not MAKE her decide to drink. You told her, and she made the decision to pursue making the marriage work. There is an awful lot of forgiveness that needs to occur in this marriage. You need serious marital counseling - but that won't work with an active alcoholic.
Your boundary was if she relapsed again you were done. Stick to it and enforce your boundary or this is going to be a rockier road than before. Dismiss the accountability and "where fault lies" questions, you both aren't at fault for what the other chose to do. You are each only responsible for your own actions.