Yup, let her stay where she is. Of course, she can walk out any time and take a cab home, but unless she's got her own funds for rehab-resort, I wouldn't shell out any of YOUR money for that. People get sober in Salvation Army rehabs.
Having to do chores is part of the therapy. Alcoholics are used to passing off their responsibilities to others. They also are often seriously lacking in humility, and having to contribute to the common good at rehab is good for them on many levels.
I don't blame those parents a bit for showing up to make sure she is held appropriately accountable for her actions. Has your fiancée even THOUGHT about how scared and worried those parents are? My guess is no--she is thinking only of herself and her sad circumstances.