Welcome to SR, M33. I'm sorry for your need to be here, but I'm glad you've found us. I was in tears reading your story because it sounds so much like my own. This is such a hard place to be in, but let me tell you my story, what I did, and how I'm doing today. Maybe that will help you out a little.
My AM was in charge of my children for a whopping two hours (unbeknownst to me, as I am on the other side of the country and they were with their dad for the summer). Apparently when my grandmother came home after that two hours, the house was a wreck, my two children running amok, and my AM so trashed she couldn't even form a coherent thought. The police were called, Child Protective Services was called, their father was dragged out of work to come get them. We nearly lost our children to the state that day.
I immediately cut off contact with my mother. It was my own family who tried to tell me that she wouldn't drink anymore if I would let her see and talk to the kids. I knew better, because she drank the entire 30 years that I had been alive, and then some. If I couldn't make her stop, then certainly my children wouldn't bear that responsibility. I ended up having to cut off other family members as a result of this. Did I feel guilty? A little bit at first. But I threw myself head-first into Al-Anon, and I learned that none of this is my fault. It never was, it never will be.
NONE OF THIS IS YOUR FAULT. Your mother drinks because she is an alcoholic, not because of anything you or anyone else did or didn't do. Please don't beat yourself up over it. If she's letting you walk out, take that inch and run a few miles. Your self-preservation and your little girl need to be your focus right now. I know it's hard, but it gets easier as you start to get your sanity back. We are here for you, so please keep posting!