Camhs will have their hands tied to an extent, if she doesn't engage with out patients but isn't at 'severe' enough risk to warrent being sectioned.
It might be useful for you to clarify with camhs when they can step in of necessary, and for future if she does choose to engage what option there are. Ofcourse it would be great if they could keep trying with her in the meantime but camhs are desperately over stretched.
It would be a good idea to find some support yourself, counciling, support group, education on sexual abuse and self harm. It's really important to learn to be comfortable talking about it, or listening to it, which isn't easy or natural for a parent.
Can you access a more supportive gp? You could ask the recepitionists to recommend which gp has experience of supporting families with children who have been abused and children with mh problems.
Can you look into charities that help? Women's aid/rape crisis/Barnardos/nspcc etc? Even if that's just support for you to then help her. And local self harm support service?
Cutting contact with any and all family who support him, or don't fully support her is essential. Back her 100%.
Look into other resources- there are numerous Internet forums for survivors of abuse, not all will be suit able for your daughter but some will. Often it can be easier to first talk about these things online, and to other survivors. There are books- one called something along the lines of how to heal from sexual abuse iirc. There will be survivors own works, from poetry to stories to songs. Try find famous people she admires who are open about their abuse, knowing other people talk about it helps. Also, and this will depend on her triggers so may not be suitable, but many of us survivors are drawn to films/tv/books that deal with abuse. They 'normalise' our experience so that we understand it isn't just us, we are not completely different or strange or alone, tha and the show better outcomes (special victims unit is a great one for this, as well as giving us the helpful language to use to begin talking about it in rl). But this does depend on everyone's individual triggers, some will equally need to avoid these.
General feel good activities, coffee out, time with friends, therapeutic sport like horse riding or other time caring for animals helps for some. Healthy self care, gym/hair dresser.
What about approaching social care services? Maybe they could find a support worker or you could self refer for a befriender?
It isn't uncommon to take alot of time to get to the stage where counciling is possible. Many of us need to wait until we are 'safe' enough to be able to talk to someone about the abuse. While controlling food and s/h are scarey for you they can often be the crutch that stop us doing worse things and keep us safe until we can cope with facing it in therapy. And while self blame is a very tough and destructive emotion in the long term, it the short term it serves some purpose and gives us the illusion of control because letting go of the idea it wasn't our fault also means facing the reality that we couldn't do anything to stop it, and therefore can not do anything to stop anyone else, everyone doing the same thing. Which is only possible to face that kind of uncertainty when we have alot of emotional safety and strategies to help/people who help.
Finally about feeling safe, in the literal sense, is there anything you can do to help with that? Better locks on the door/security camera/rape whisle? Dog that would comfort and help protect her? Female only self defense class? And do tell her dv or rape is often why women attend. Can police or social service do anything to reassure her about safety?
Good luck. Best thing you can do is support her and believe everything she tells you about this.