Sorry to hear your story.
From my experience with infidelity and alcoholism, and alcoholism in general, is that the healing process is quite linear. Right NOW nothing has priority over his fix. This is why I – as a cop – was arresting drunk parents with their kids in the car. The fix was the main issue, family second. If an active alcoholic has a choice between one more drink or making it home for dinner… the drink will always win.
Until he has his addiction in some form of control there is no way he can make any fruitful contribution to your marriage. At best he can not cheat, and that’s about it.
If you are up to it and want some hope for this marriage then IMHO your best bet is to accept that for the next 60 days the ONLY goal is sobriety. Not bare-knuckle, I-will-be-dry sobriety, but daily AA, sponsor, detox… a PROGRAM. A defined plan with daily goals. Once he’s detoxed his body and started clearing his mind is the phase where he might be able to work on the marriage.
I encourage you to look into Al Anon. Chances are this stiutation has already heavily impacted you.
I also encourage you to understand the hereditary power of addictions and talk to your kids. For each year they remain sober, the lower the probability of them becoming addicts too. Like… if I was alcoholic, and my son started drinking at 18 there would be something like a 50% chance he would eventually have to deal with his own addiction. If I could delay it to him being 22 years, that lowers to maybe 20%.
"If, therefore, any be unhappy, let him remember that he is unhappy by reason of himself alone." Epictetus