Hi Spirit, You are a good mother and this is not your fault.
I think talking to in-laws might not be good for you right now, unless you tell the woman you won't stand for any judgment from them.
My daughter had a sui attempt at age 14 and was cutting, that was 4 years ago. I'll never forget the doctor telling me I don't have to try to talk to her about it, just be there for her, and to play. Play boardgames or try to do fun things. And I had to work on myself and my guilt and anger and depression. Like the others said, she is in the right place, you did the right thing. She will have group therapies and healing activities. You must think positive, this is so much easier said than done, but you must think positive that she is getting help and will get better.
Try to make sure she gets to the therapist weekly (when she comes home), and a therapist for yourself as well if you can. My daughter's pdoc knows about the cutting and doesn't always admit her to the hospital for it. My daughter has been hospitalized twice, and my 16 yr old son has bipolar, also a cutter, and has been hospitalized at least 5 or 6 times, geez i'm losing count.
And maybe she will develop a mental illness, but it's not your fault. We are all just trying to live our lives and find happiness. This mental illness stuff just happens, and other things happen to people too that aren't fair, far too often. Try to be resilient and don't lose hope. Hang in there Mama, and keep posting.