Old habits are hard to break. If he is used to using alcohol to mask stress, then it would normal for him to reach for the bottle during those times. It's very important that he have good support and a recovery program. You say he is going to meetings every day and has a sponsor, which is good. Unfortunately, there's not much you can do if he chooses to drink over the over the chaos his ex is causing. Hopefully, he will reach out to his AA sponsor if he feels like he wants to drink. The more he resists the urge to drink, the easier it will get. If he knows that she is attempting to sabotage his recovery, hopefully he won't let that happen.
Also, it might be good for him to see an attorney about his legal rights regarding his daughter.