So you are in a relationship with someone who is in a bad spot, turns to alcohol and random sexual encounters to cope, is in a messy relationship with her family (maybe), and has already cheated on you. I say maybe because you're getting all this information from an alcoholic who has already been unfaithful to you.
What here is worth saving?
She's worth saving? Yes, she is. But that's something you can't do for her. She's got to save herself. You are also worth saving. Lucky for you, that's something you can do yourself.
You didn't cause this, you can't control this, and you can't cure this. Shed all fantasies you have of providing her with a safe place to land. Active alcoholics need people that think this way. It feeds their alcoholism.
It's been my experience that my investment in other people's problems is usually in direct correlation with my unwillingness to deal with my own life and my own problems. Openly and willingly jumping into the open water with someone who has these dead weight problems tells me that there's something going on with you that maybe you should deal with yourself. That's not a judgment. I've been there. Save yourself! It's a sign you aren't willing to go down yet, having reached out for support.
There's a lot of support here. Hang out and keep asking questions. Some of the answers you get will be harsh, but they are usually based on a lot of pain and experience. Such is life.