Op, you have my sympathies.
I have a friend in exactly the same position as you, only my friend is the Nan.
Well done for seeking answers - here or anywhere - over how to help this girl.
My friend's son on the other hand, has allowed his new wife to kick his bereaved daughter out of their house due to her terrible behaviour. In my view, HE is spineless and his wife is the 'specimen'. She doesn't give a shiny shit about her step-daughter.
You obviously do though. Good on you for standing up to the criticisms you've received.
BUT. You have to accept that you are not a child psychologist and you cannot meet her needs.
Most importantly, you have to accept that you cannot force your bf to help his daughter. You cannot make him see that she needs counselling and really good, possibly long-term therapy. You are trying and you want to - at least, that's what comes across to me in your posts.
But you can't. He has to want to see the problem and desire to help her.
For what it's worth, my friend says the reason her son won't do more for his poor daughter is because he is afraid that social services will remove her from him altogether.
Crock of shit. Fact is, he's married to a woman who wants the girl to disappear.
You have two options: continue to be anxious and to urge your bf to get help for her (which doesn't seem to be working - because he isn't doing that in any meaningful way, is he) or pack him in and breathe. This lass isn't your problem. He's your spineless boyfriend's problem and you can't buy backbone or make it. 