marie 
We met with DS2's teacher today because of some ongoing behavioural shit that culminated in a violent scene towards his brother yesterday (they are 11 and 12 respectively). We also have 2 younger children whose safety is of course important to us. His teacher said, and I quote, "I don't recognise the child you are describing" as he is well-mannered, attentive and happy in the class room with no concerns about his learning.
At home we have a destructive, unhappy child, prone to violent outbursts, very difficult to live with. We are seeking help for him and us - again.
The point I'm trying to make (and obviously our situations are VERY different) is that it is sometimes astonishing how differently our offspring can behave when confronted with 'strangers' rather than their own family.
Give her 'host' family a chance.
Give your DD a 'chance' to prove herself.
Give SS a chance to show that they are able to support her.
I have no idea how hard this must be for you, but do you see any other way at this point in the proceedings??
My DH moved out from home when he was 17, he was not 'troubled' (well, no more than any teenager, I suppose
) and it was the making of him. Again, that means squat for your DD, but much as 17 is young and can be maturity-wise very young, she is not too young to make choices, even they are bad ones (and I don't think that moving out was the worst of choices tbh as things were so fraught between you).
I so hope that things will work out for her and for you and that with time the relationship between you two will be a closer one again.