I agree with everything everyone is telling you. One other thing to consider. If she moves in with her boys, how do you kick her AND them out? You might have the heart to send her on their way, but would you have the heart to kick them out of "their" new home? Better for them to stay where they are, and let their dad look out for their well-being, than uproot them twice.
I see absolutely no readiness on this woman's part to quit drinking. And if she hasn't lost her kids while she's drinking, she isn't going to lose them because she's in treatment.
You sound like a nice, caring person--just like all of us are. And you can't "save" her any more than any of us have been able to "save" the alcoholics in our lives.