Can you move in with your Dad for a little while? I'm thinking your mom doesn't even realize what she is doing. Right now she's thinking about your sister and thinking that you are just being a "brat".
When you are gone she will really think hard about what was going on. It may take awhile but she will realize that she's hurt you. As far as your sister maybe you can tell her doc about her drug problem, maybe he can talk to your mom & sister about it and get your sister help. They don't have to know it was you that said anything.
Good luck I hope that you can figure out life in general. I would say get out as soon as you can. Maybe a friend has an extra room that you can live in for cheap until you find something else. Or take the offer to go live in TX for a little while. I mean if the bf is going to be away WHY do you need to stay in NJ while he is gone. Just my 2 cents. Good luck to you.