Does your daughter see a therapist? If so have you spoken to them about the options and what they thought? If she is seeing a therapist, maybe that person can see a different picture.
Myself, I would have a very difficult time leaving difficult child alone. But I know that if I were there, difficult child's response and willingness would not be the same. He would end up pulling me down and making me feel bad at some point. I know this is a difficult decision. When is visiting hours? Is it daily? Weekly? I definatley have the experience with the anxiety. Do you think the anxiety plays a big picture in the eating? Personally if we were dealing with difficult child and he had anxiety about something, there is no way we could get past that. If the anxiety is treated as well, it may help in the treatment for the eating disorder. This has got to be a difficult decision. Sending good thoughts.