I have an alcoholic mother too and I am a recovering alcoholic. I understand the pain you feel. Welcome to SR.
From experience, you could try waiting until she is hungover and go to see her. Don't say much but ask her if she wants help. Say to her "Mum - why don't you get some help?". Say it with love and then leave.
I have heard a few recovered alchies who came into AA after hearing those words.
Please don't have any expectations though. And please remember that NONE of this is your fault. You don't have to do a thing - except to take care of yourself and learn to love yourself. I think a meeting sounds like a great idea btw.