Sticking by your boundary and having him live separately is OK no matter what he does or does not do. It is a boundary and a date that takes care of you and your daughter. You do not have to adjust your boundaries based on small steps that he takes. It must be so exhausting and stressful watching his movements to see how you should respond.
Him living separate is not giving up on him or punishing him or being mean to him. It is a consequence of his behavior and actions - a natural, normal, expected consequence. You are simply being responsible for yourself and your daughter and requiring him to be responsible for himself. He'll either move out and do what he says he wants (find recovery) or he'll move out and continue drinking.
One thing I feel is certain based on my experience and what I've seen on these boards - separating does not cause people to abandon recovery. Maintaining the status quo does not jump start recovery, encourage, or result in greater recovery efforts.
If he moves out the year following that will be very revealing. He'll either embrace recovery or not and you can do the next right thing as time goes on. It will be much easier for you, IMO and IME, to do the next right thing if your home is one of peace and ease - where you can focus on your wants/needs - not watch his and wondering if what he is doing is for real or for show or if he is asking the right questions or following up on his other issues etc. etc. It all becomes part of the dance that keeps you both stuck in limbo.
FWIW I asked my husband to move out for a year and work on his recovery. I promised to go to marriage counseling if he was in active recovery after 6-12mos. He flipped out - which was very revealing in and of itself. He had no intentions of changing. The treatment program he ran off to was a vacation from the emotional trauma and panic of me asking for a divorce. He made some phone calls and did some stuff that was done in the name of recovery but his only intent was to maintain the status quo. His goal was not to quit drinking, it was to preserve his enabling relationship.
I do not think my xah is a bad man either. He was not abusive until I asked for a divorce and I think he loved his family but he was an active alcoholic. At the end of the day addiction is what he protected and living in a home where one person is protecting the very thing that is destroying it is no way to live.