Hi gaby. I'm sorry to hear things aren't any better. I can hear how distressed you are. :(
I think some kids - and it seems your DD is one - go through a few years where they are really hard work - just basically difficult and often unpleasant. I don't think it's personal - tho it certainly feels like it. It is part of their 'natural' process of growing up and separating from you emotionally.
You are very focused (quite naturally, as her mum; most of us do it) on trying to change her. But it's impossible: you can't actually change anyone else - you can only ever change yourself. This is actually true of absolutely anyone and everyone you meet in life, but IME we seem to forget it when it comes to our own children! I think you need to step back from trying to change the way she behaves and focus instead on your own responses.
Firstly, you really, really need to detach... When she says "I hate you", you need to avoid rising to the bait at all, and mutter something like "That's a shame dear"... And if you manage that a few times, it will become easier, and eventually you will find you do actually get hurt less often.
Also (and I know this is much, much easier said than done) you need to ignore being told you are a 'bad mum'. IME, many teens and almost all exes try to use this against us at some point.
They know (maybe unconsciously) that if they make us feel bad about ourselves, then we're easier to manipulate. My standard response to my DS, when he went through his stage of telling me I was a sh*t mum, was to say "Oh I know, but unfortunately for you I'm the only mum you have... If you can persuade anyone else to have you, let me know.."
Secondly, I think you need to sort out some counselling for yourself. Go to your GP and ask her/him to refer you. It is really, really hard dealing with a 'challenging' teen, and you will cope much better if you can talk to someone and get some 'neutral' support.
I also think you need to be nice to yourself. I have probably said this to you before, but you need to do some things you enjoy, make yourself laugh, go out with friends, treat yourself to a massage, go for a long walk, exercise... Anything that you like doing. Looking after yourself is not a luxury; it's a survival essential: you will cope much better with your DD if you also have plenty of lovely, fun things in your life.
If you think about it, if we forget to be kind to ourselves and focus all our attention on our DC rather than ourselves, we are actually giving them a very powerful negative message: we are in fact showing them that we ourselves don't really think we are worth much, and that they are far more important than we are.
So when our own DC then act like they are more important and we are not worth much, it's not surprising: they are actually just acting out what we have shown them!
:(
On the other hand, if you look after yourself, do enjoyable things, and generally are kind and respectful towards yourself, then you are showing them how they should also treat you. Because you're worth it! 
Does that make sense?!