One thing that may be getting overlooked here, if mom is receiving any form of structured aid for this daughter such as child support, SS Dependent's allowances, Food Stamps, anything that calculates income on the basis of the number of people in the family, or based on this child being a part of the family, she is NOT likely to let you go easily until you are 18, because she is getting part of her income based on your being included in her family. You're a cash cow in this case. This could very well be the reason she moved and changed her living arrangements a while ago and started actively parenting again. Or maybe, she was just trying to do better. In any case, yelling at you every day and not letting you use the car are NOT likely to be considered serious abuse such that you'd be removed from the home.
That you "don't want to involve the police" with your home situation is sort of a giveaway that it's not bad enough to classify as realiy serious abuse. If you'd rather be where you were, in all the verbal and emotional abuse, than be in juvie (or anywhere else, except this place you want to run away to) that's going to be something they consider in trying to judge whether you are really being abused. Would you rather, given the two choices, spend your time these next 8 months at home with your mother or in a foster care placement? You can bet on it, if you leave to stay with friends, the minute your mother gets involved and the police get involved, those adult friends/parents of your friends, etc. will go right along with whatever the police and your mother want done with you. Without her cooperation and permission, you are in a sort of problem situation in which you need to hold on for 8 more months.