Firstly, you say you've got no coping skills, well that's completely understandable from what you've been through. However, it takes time and effort to improve these. I think the best place for you to start is make some friends so that you have people to talk to every day and share your thoughts with. Obviously this isn't an easy thing to do, and requires courage, but once you've started talking to people, you'll find that more people will approach you, so it won't be as hard. You have a boyfriend, so why not make friends with his friends. It's definitely a starting point, ask him if you can hang around with him and his friends, and as he introduces you to them you'll start to make friends and this will open doors and make it more comfortable for you to make other friends.
I'd also consider actually going to the therapist. This will benefit you because you can let out your thoughts and anger to the therapist who will help you cope with it so that you don't have violent outbursts. You need to manage your anger and stress, and you can't do this alone. There is only so much a friend or boyfriend can do, a professional therapist can offer more specific advice. On the positive side this will also make your mum happy, so that from there you can start to improve the relationship between you and her. She cares for you, no matter what you may think, you are her daughter and she loves you. That's why she wants you to see a therapist, because she's concerned and wants you to be happy. It might be difficult for her having to attend, and at first it will be strange. But there clearly are problems between you and your mum and therapist can help sort that out. If it's such a huge deal can you not find another one, or perhaps some other counselor that doesn't require a parent to attend?
I think in any case you might as well give it a shot. You've got nothing to lose by trying, but the thing is, it only works if you try to talk sensibly. There is no point in you both going and all you're going to do is argue. It might release tension but you might just get more angry at her for not listening or not taking your side. Listen to what she has to say and talk to the therapist, explain why you don't think she's fair or what she said is wrong. The therapist can help find out the cause and help to fix it. You both have to try to make it work, otherwise the whole process is useless.
It's also important to have a positive outlook on things. I know at this point it seems like the whole world is against you and the whole world hates you, but you have to put in some effort to show them what a person you are and go out and make friends. Do fun stuff with your boyfriend to improve your happiness. Go to the movies and watch a comedy, something that makes both of you laugh to get away from the stress and anxiety. Like I said, learning to make new friends is not easy, but once you've started it, it gets a whole lot easier. Having friends enables you to be more sociable and this will often than not make you more happy and fun so that you're not constantly thinking about what's going on at home.
I wish you the very best of luck, and if you ever need to talk feel free to PM me anytime!