What do you think the residential treatment center will do for her? She sounds more like she has some sort of disorder than that she is a kid heading for trouble. I think she needs help more than discipline. Has she ever seen a neuropsychologist for complete diagnosis? I have had terrible depression and discipline would not have helped me. May have just made me give up completely.
Poor hygiene is often a sign of autistic spectrum disorder, high functioning.
Think hard about what you want to accomplish and ask about it with Residential Treatment Center (RTC). See what kinds of kids are there. See how often she gets to see a psychiatrist and ask if she will be totally evaluated. You don't want to treat something she doesn't have nor ignore something she does have, but was just missed. The right diagnostician is the key. I like neuropsychs best as they test in every category, for every disorder, and not just for school performance.
If it were me, I'd do the neuropysch evaluation first. If she has a disorder, an Residential Treatment Center (RTC) probably will be a bad fit.