Hmm. This is obviously as you say a deep one to sort out. I don't think MNers are going to be able to sort it during a few posts but the main thing I want to say is that NOW is the time to completely open your mind to ideas and suggestions.
Otherwise, as people I meet through work do all the time to me, you'll simply feel "nah, tried that, it won't work" and i think this mindset 'seeps' into your whole attitude and subliminally your brain accepts messages that this isn't possible to change.
Usually when things are this bad it's because a downward spiral has started, it's so easy for families to do this because of the fact that kids often are 'sponges' for atmosphere and will give back what they get, but double it for luck! Then quickly people find the positive times have all but disappeared.
I'm sure there are lots of things you could do to help, lots of little strategies but maybe it needs to be in a more organised way in order for you to feel in control of it? Try approaching your GP for family therapy, I KNOW you've tried it before but try another therapist and bear in mind your daughter is older now so things may be different.
the fact that she can sustain things at school makes me think that this problem is about the family, not about her. Try to think of it that way - not that she has behaviour problems and her brother doesn't - it's that the family has a problem getting along together sometimes.
If it was ever felt that these issues were to do with her particularly your GP would be able to refer to the local Child and Adolescent mental health team so there is deeper help, or should be.
I still think though you can get there with her. I think the key is trying to turn every interaction with her into a positive one and to give her some one to one attention with you and your DH where you focus on her in a positive way.
Just a thought, maybe a silly one but trying to help, would you be able to be a classroom helper in her class for a morning to see her in her positive environment - might be a key to a little inroad of positivity for you with her!
I would just try things like this alongside asking GP to refer for some family input. If it happens though, definitely make sure BOTH kids know it's about all of you, not about her. And personally I would present it as someone helping mum and dad to keep the family happy.
Sorry it's long but wanted to try to help, obviously you'll have lots of opinions on here so go with your gut on what's right, won't be offended if written off as load of rubbish! one thing I find on here is that on the same issue there are one million ways of attacking it. The main thing is that you can't go wrong by TRYING to address it, better than not trying!