Is it "we", or is it you that tries to speak to her Mum, though?
You put her and your house at risk, luckily it was the house that got it. She could have had the house stormed by older Teens and been sexually assaulted etc.
Your DH needs to get his head out of his arse and speak to her Mum, not through her, no wonder she is having issues, that's way too much to put on a child.
She was probably scared, thankfully she called her Mum.
You can't trust Teenagers, you hvae to be the one in charge, it gives them confidence and a backout, by being able to say that they can't do something.
To give a child who is having social issues keys to your empty house is ridiculous, wtf, were you thinking? When I went away and my children stayed with my Mum, my Mum got the keys, not my children.
Your DH needs to start to see her for what she is, a sacred, insecure, hormonal mess.
Start forming a plan between you all, before it's too late.