My mother is an alcoholic and I'm very frustrated with her behavior.
What is she doing that is upsetting you?
When she was drunk she hit me and called me names.
I'm sure you're really frustrated with your mother's alcoholism and it's acceptable to be frustrated. You should tell your mother how you feel and try to get her to seek help. She will never get better on her own, she needs your help.
She just makes me so mad when she does this.
I think that it is right that you are upset with her. I really think that the way to go would be to try to talk to her. Let her know how it effects you when she drinks that much.