It sounds to me like you and your mom are an awful lot alike. You both think the other person ought to be doing something about the situation. She’s stubborn. So are you. I do appreciate how hard you are trying to work things out. And I especially appreciate that you would rather have a good relationship than material things. That speaks well for your character and heart.
As you’ve already found out, the strategies you’ve been trying aren’t working. So let me make an alternate suggestion. It’s not new information that your mother gets upset when you try to get her to listen. It’s also not new information that she can’t stand to lose a fight so escalates it instead. The best thing a person can do in that kind of situation is to stop fighting.
Do you know that old game of tug of war? People get on either end of a rope and pull. The team that pulls the hardest usually wins. But another way to “win” is to let go. The other team can’t win if you’re not playing.
Instead of trying to change your mom, I suggest you focus your energy on learning how to manage your feelings. If you find yourself getting hooked into a fight, take a deep breath, apologize for letting your temper get the best of you, and respectfully suggest that the two of you talk at another time. Then leave the situation. It’s good practice for you. It will model for your mother how you would like the two of you to relate.
Meanwhile, you need to find a better group of friends. Everyone needs people to talk to who understand and support them. Think about joining a sport or club or volunteer at a project that interests you. People who join up to the same things usually have things in common. Start being friendly and you’ll probably start finding people to hang out with.
I also suggest you start finding other adults to talk to. It could be a relative or a teacher or a coach or the mother of one of those new friends. That person can give you an adult perspective on things without the emotional overlay of a parent. I suspect that when you drop the fight and find other ways to siphon the stress out of the family some, your mom will be more able to manage your feelings and your opinions.
While you are building a network of support for yourself, I suggest you consider using one of the online or phone warm lines when you need someone to talk to. The Boys Town Hotline has counselors on duty 24/7 to talk to teens who are feeling depressed or who just want to sort things out. Yes, they talk to girls too. The number is 800-448-3000.
I wish you well.