You and your mother should both go see a therapist together and get advice from them about what to do. I am neither a psychologist nor a realized master, but my opinion on your sister is this, to put it simply...
She is seeking to establish her self identity and obtain a sense of power and control. She lost her sense of power when she was abused, and probably her sense of self. She needs space. Let her do what she wants. She clearly cannot be controlled and continuing to act like she can is just perpetuating an illusion, the sooner everyone stops trying to control her, the better. Reinforce whatever is good in her, such as her dreams, hopes, aspirations, and so forth. Keep silent about things you disagree about, don't argue with her, condemn her actions, judge her, or let her draw you into drama. If you reinforce whats good, and keep silent about whats bad, she will feel like you see the good in her and accept the bad. She will feel accepted for who she is, which will help her obtain a sense of self. It will also establish trust in you, which in turn will act on her unconsciously to be more susceptible to agreeing with what you say or have said. Thus, since you've already suggested therapy, she might come around and decide she needs it, and even think its her own decision.
You should refrain from telling her what to do, from judging her actions, even with the intention of helping her. You've already tried that and it hasn't worked, shes not listening. She goes to these other people for support because they don't judge her, don't try to control her, don't tell her what to do, don't pressure her to see a therapist, so she feels accepted. Even if you were abused as well, everyone handles abuse differently. For many people it comes with a loss of a sense of power, and later manifests as rebellion and seeking to establish ones power in unhealthy ways. So she needs to be allowed to do that.
Cutting her off completely would be bad. In addition to supporting whats good and refraining from commenting or judging whats bad or that you disagree with, you should stay in touch with her. Facebook her, send her gifts for her birthday or Christmas. That way when she comes to her senses, she will feel she has someone she can go to. She won't feel like her family has disowned her, in which case she might just go further down the spiral.
I also highly recommend and strongly
suggest you read this book: http://www.amazon.com/Reviving-Ophelia-Adolescent-Ballantine-Readers/dp/0345392825
It will help you get some perspective on this situation from a more universal angle.
In addition to that you should meditate on this situation as universal, many people go through this, many young girls, many sisters, many families. Its happening everywhere, its because of how our society is set up, because of how much mental and emotional problems everyone has. A man abuses some young girl, or something of that nature, because of his emotional and mental problems, and she in turn develops mental and emotional problems. In both cases the people are suffering, and in both cases the peoples suffering usually arose as a result of either prior abuse or a broken home, or both. Its a pattern, and its widespread.
Also meditate on the fact that the condition of the normal deluded mind is, as you said, confused, afraid, running from the past, not wanting to face past trauma. Thats the natural condition of most people to a lesser or greater degree. Different people handle it differently, but if you see someone you think is "normal" don't think they are any different than your sister in this respect.
Your anger is because you don't understand why your sister is doing what shes doing. Intuitively you know its because she was abused, but you don't understand the karmic causes and conditions that shaped her into what she is today, into how she is acting today, so its upsetting. Reading that book will help, reading other books on psychology will help as well. In addition to this, meditating on your own mind, the way it works, and becoming aware of all your subtle delusions and so forth will help immensely. But you have to be willing to fearlessly acknowledge yourself. The better you know your own mind, the better you will know the minds of others. Our ultimate nature and mind is that of Buddha, and since everyone shares this nature, the closer you get to your ultimate nature, the more you will naturally understand how everyone around you works.
Psychology is more or less the study of the causes and conditions that lead a person into certain psychological states. We can frame the whole thing in terms of Buddhism to a limited degree, and say that psychology is the study of how the aggregate of the self is shaped and formed by the aggregates of the six senses. In psychology its known that certain events, for example, are likely to lead to PTSD, while others are likely to lead to depression, and others to some other problem. Its the observation of the formation of mental habits and patterns, so in my opinion its a valuable thing to learn. Pop psychology is mostly useless, and while many people like Jung, its not really useful in terms of trying to help people in a direct manner. Basically Jungian psychology is not primarily concerned with how an individuals abuse leads to behavior later in life.