Once the alcoholic gets called out on their behavior in your case giving them the choice of rehab or the road they become bitter and resentful toward those that won't tolerate or enable their behavior.
Also I hate to say it there are/were other issues before the alcohol became one including regret.
Keep in mind the alcoholic or drug abuser will not change or sober up until they really want to and not just to appease someone else. This trip to rehab could wind up being nothing more than a timeout/break.
Hope things wind up working out positively but in the end the 12 year old is the number one priority now.
Good Luck