What should I do about alcoholic mom?

I am 30 years old with 4 young children. I am married and have a normal life. I was raised by my functioning alcoholic mother and was taught by my grandmother to never really talk about it or acknowledge it. Anyway, over the last 6 years I have allowed my mother to babysit my kids, drive them around and take them for the weekend. About 90% of the time (that I know about) she got drunk with my kids. The last time my mom babysat, she passed out drunk while with my 4 year old. I arrived at my mom's house and my daughter had to open the door for me. She was crying, saying that grandma fell asleep and she wouldn't wake up. I finally put an end to it, telling my mother she is no longer allowed to babysit or even be around my kids (ages 6 to 6 months) without me. My mother hates me for this. So does my grandmother. They blame me for my mother's alcoholism and call me a bad mother. My mother has always been emotionally abusive, but it is getting worse as I get older. I cannot deal with the abuse and arguing anymore, so I stopped talking to my mother. I am at a point now where I cannot handle all the stress this places on me. My mom is not apologetic and thinks she has done absolutely nothing wrong. She admits she has a problem, but believes her drinking has nothing to do with our strained relationship and blames me for it. Yesterday she called me and left me a message, asking for the kids' social security numbers so that she can take me off as beneficiary to her assets and make the kids sole beneficiaries. She always takes a bad situation and makes it worse! I don't know what to do anymore. Should I try (again) to salvage what is left of our relationship or just cut all ties with her? She is never going to quit drinking and will never forgive me if she cannot be left alone with my kids. If we continue to talk, we will always argue and I will always be blamed for all her problems. Please help!