Hi, I'm sorry this happened to you. My husband grew up with alcoholic parents. He has many stories similar to this, where he was humiliated in front of his friends. Unfortunately he grew up and became an alcoholic. I am posting to tell you about my experience, because although things came to a head for us when he became an alcoholic, it made me look at my own upbringing, and see things as they really were. To cut a long story short, we had a tough time together, he sought treatment, hasn't touched a drink in a long time and we made it though the other side.
I wanted to share what I learnt that might help you. At the moment, you may feel like you are hurdling from one unpredictable disaster to another, with a sense of confusion and a feeling of being completely lost. That was me, for years. I nearly started to crack up, until I realised I can only control....me. I had to set my own boundaries.
For you, it might mean having plans ahead of time for things that will involve your mother. Such as, no more invitations to things with groups. I get that it is sad, and you want to involve her in things, but in my husbands childhood, everyone tried to pretend it wasn't happening, and just did things as they normally would, and then were all completely surprised when it all ended in disaster.
If you want to do things with your mother, there has to be an exit strategy. Such as, you all arrange to go to the park (whatever) on Tuesday. If you arrive and she is unable, be prepared for that, rather than shocked and disappointed. Immediately acknowledge it "I see this doesn't really suit you right now, we can do it another time", and leave without confrontation.
You may one day have to have an honest conversation with her. No point confronting her, accusing her, blaming her, she won't respond. Talking about you, rather than her, might be the only way to get through. Talk about your family and whats best for you.
Finally, and this should probably be the first thing you do. Go to Al-Anon. Its for family members of alcoholics. My "first" meeting, I sat in the car park and was too scared to go in! I felt like it was an acknowledgement that I had no more answers, and had no other place to turn. My real first meeting, I finally went in, and it changed everything. There is no pressure on you to talk, you can just listen. And you'll here stories that you'll think to yourself "that's just like me". It helps. It was at the point that I went to Al-Anon and also got counselling, that my husband saw I was changing and controlling what I could, that he looked harder at things and sought treatment for himself. I feel for you, and I hope things get better for you.