I must say you are a patient man. I have gf who has been patient with me for many years, BUT I never got to the point where it became a weekly incident. This last incident she said it was her last time, and that she was going to leave me. She still may, but it was also my last straw with alcohol. I cause harm under the influence that I don't want to do it to anyone, especially not put her through it.
She has to really want to stop! I really want to stop I have stopped and I don't see myself coming back for a long time, and most likely not ever! I chose to rid everyone of that person, but it was my choice. If she is serious she will do it without your help.
Honestly though, she knows you will take her back so she can get away with "murder" and it would be okay with you. Don't let her do that, and if she really loves you I promise she will stop in a heart beat! But don't give in so easy, and you probably don't want to spend the rest of your life dealing with someone like her... I should probably do my gf the favor and break up with her; she deserves better than I have been. You seem like a good man, you can find anyone, don't waste it on someone that will bring you hardship.
I wish you the very best. Although I have given you a recommendation, you will do exactly what you will do, but I do hope its a right choice.