I'm sorry to hear about the situation your sister is in. What I would recommend is this:
1. Pray for her as a family. Rosaries, Masses, etc. are all great and necessary, and fast for her too. Go to e5men.org to learn how to do this.
2. Deepen your friendship with her. I once heard a saying for parents that if you talk to your kids about everything, you'll be able to talk to them about anything. So, take a deeper interest in her life: not only in her dysfunctional relationship, but in her shoes, her school, her interests, etc. This way, you earn the right to be heard by her, and she will not feel as defensive if she can see you as more of a friend.
3. Get closer to Jesus yourself, and continue to set a godly example.
4. When we do these things and yet nothing seems to happen, we often wonder what we are doing wrong, or what we're forgetting to do. What we need to remember is that God is answering all your prayers, and giving all of the graces of conversion to her. But God has also given her the gift of a free will. When she does turn her will to God, then all these graces will be waiting for her. See the mercy and patience of God as an example. Keep up the prayers and love and do not let go of hope. She needs to know she can always come back.