How to help an alcoholic?

Hi. My Mum is an alcoholic and has been for a long time now, however things are getting worse. I have a child of my own and due to my Mum being drunk around my daughter I have decided that until my Mum can be sober around her I wont let her see her anymore. I'm lost with how to help her. I know she is depressed and that it is an illness. She says she wants help but will only accept certain types of help on her terms. She wont see her doctor and only wants to be put in a private rehab centre which we cant afford. She blames everyone else for her illness and we are getting nowhere talking to her because she is so unreasonable. Has anyone got any advice that has worked for them? Am I doing the right thing by not letting her see her granddaughter when she is drunk or will that make things worse as she delves deeper into depression? Thank you for your answers.