I am so sorry that you're having to go through this.
I see here (from reading your post) a strong young girl that is determined to make a life for herself no matter what her mother says or does. You should be proud of yourself for being such a strong girl.
Your mother, by the sounds of your description of her in your post, sounds like she's got some addictions and demons of her own to deal with. I think the best thing that she can do for you is for her leaving the state, for now, until she gets her act together; if ever.
You seems to have a good home to live in with your sister and her family. Stay there until you real your goals in life. You are an amazing young lady, please be proud of who you are.
I too have been on my own since I was 16. I know it isn't easy but, it can be done and you can have a productive life in the end of it all. Like Duke said, surround yourself with people that love you and you'll be fine.
Also, it might not hurt for you to go and talk to a councellor about things that bother you with your mother. it might help you to put things in their place so you can move forward without dwelling over the "ifs, and or buts" about why this is happening to you.
The best of luck to you always and I know you will succeed into adulthood. You will survive because you're a strong willed girl. have faith in yourself darling.
