You probably won't want to hear this, but the only thing that can fix your mum's drinking is your mum herself, and time. My dad has had a drinking problem for years. He has been on various medications from his doctor, has been to numerous help-groups and has had my mum going on at him for all of this time and none of it worked.
However over the past few weeks he has, by his own decision, started going to a new help group and is now finally doing something about his drinking. The only reason this has suddenly happened is because he was finally ready for it, for whatever reason. It's not just about wanting to stop drinking, your mum will also need to be at a stage where she feels able to stop drinking, where she feels like it is something she can do without breaking down or losing it. Alcoholics must help themselves in their own time. Anyone who is not or has not been an alcoholic can never understand what an alcoholic goes through.
People on here have mentioned things like counselling and support groups. Yes these things do exist, but there is no point in trying to force your mum to go to any of these things, she must make the decision for herself in her own time. I have been there and I do know what I am talking about.
This probably doesn't help your situation with your mum this christmas, but I hope it gives you hope for the future. One day your mum will be ready to sort her problem out, but nobody can force it. All you can do in the meantime is accept her problem and do what ever you feel is neccesary for you to be able to cope with it.
You can pm me too if you need to chat.