Desparate, I'm sorry that you find yourself in this situation. You have the right idea, think what you want to say and write it down. It shouldn't become a list of all your mothers transgressions, but something that tells her how her drinking affects you, your realtionships, and your family. And give her the letter after you've read it to her. She may not want to read it at first, but after reflection it might help reinforce what you said. And understand that your mom is sick - she is probably not going to want to listen what you have to say; but she needs to hear it. Just speak from the heart and see where it leads.
Please understand that dealing with alcoholism is a marathon, not a sprint. Your mom didn't become an alcoholic overnight, and she will not recover overnight either. But people recover from this disease every day, it just takes a lot of desire and effort.
Good luck, and keep posting.