Let him move out and let him fill out the papers. Focus on your sobriety. Are you going to AA meetings? The support there is incredible.
If hubby doesn't want to work on the marriage, let him work on the divorce. Seems to me you have a win-win situation with this guy who wants YOU to do everything. Did he ever do laundry? clean the house? cook dinner? participate in the marriage? I don't want to be harsh, but there are many spouses who take advantage of their wife/husband and let them do all of the work.
Focus on you, let him do what he needs if he's that unhappy.
You stay strong and stay stopped! Sobriety--you are so worth it and you are worth letting go of things that aren't supportive of your choice(s).
Love & hugs,