I can tell that this situation is heartbreaking for you and your mother and that you are genuinely confused and upset by your sister’s behavior. Without knowing more about the situation, I have only one guess. Is it possible that your sister feels that everyone has abandoned her? You and your mother both got out of your father’s house. She’s been left there – with the violent crackhead that you couldn’t stand to live with!
I’ve known situations like this where the father is also abusing the daughter and threatening her not to tell. If that is possibly the case here, of course she can’t tell. She has to hope and pray that you will guess. Her various negative behaviors could be seen as signals to you that she’s needing help.
My best suggestion is that you stop blaming her for not being “an adult” and see her for the scared 16-year-old she is. She may need your help, not your negative judgments. You and your mom need to discuss a way for her to not live with your father if that’s what she needs.
Pick her up, take her to a safe and pleasant place and have a sympathetic heart-to-heart talk. Apologize to her for leaving her with your dad and ask her as kindly and calmly as you can if he is hurting her in any way. See if she would like a way out of the situation. Be prepared for her to be angry with you. She may well have a right to be. Listen. Don’t defend. Just listen and be there for her. If I’m right about the situation, it will be important for you to be as supportive as you know how to be.
I wish you both well.