I'm sorry you're going through this. it's very common for alcoholics to weasel their way back into our lives with promises and then not follow through.
What was your boundary, precisely? You will let him move back home if he goes to AA regularly and stops drinking. And if he broke either of those boundaries.....what repercussions did you tell him would happen? Was there any sort of time limit -- he has to start AA within a week, a month?
If none of that was ever truly clarified for him, maybe now is the time to do it. Specific actions, specific times, specific boundaries, i.e. what you will be forced to do to protect yourself if he doesn't follow through. It will then be his choice how to proceed.