I just want to chime in that BS, unless it’s a therapeutic school, is simply not the place for a girl who already has an eating disorder. Boarding school is a breeding ground for disordered eating. Pretty much every girl I know at boarding schools across the US has flirted with disordered eating.
I hope your family reconsiders for your sister. I can’t emphasize what a bad idea I think it is to send a mentally ill kid away to boarding school.