It seems to me that she owes you an apology but I agree with C.O.D. that getting an alcoholic to admit they are responsible for any problems is virtually impossible.
There are some things I would not be able to forgive and affairs are one of them. Of course what you decide to do with this relationship is up to you. Do you think you can trust her again? For me that would be a big problem.
I kinda struggled with axbf in trying to control him. When I realized it was virtually impossible and started distancing myself from it/him, things just fell apart because he said I was no longer meeting his needs. What he really needed was for someone to accept that he will drink and smoke as much as he wanted to, and I was not that person.
Anyway it has all been very painful but also quite liberating. I realize I am still clinging to the past and that is the final piece I have been trying to let go of. After this I'm not sure I want to be in another relationship for a while.
good luck whatever you decide.