You've got me. Alopecia areata doesn't have scaling, and doesn't affect other parts of the body with scaling. Psoriasis and the like does cause scaling but doesn't cause patchy hair loss. If the doctors have done biopsies and offered treatments that haven't helped, then there's not much I can add from a distance.
One question: Does your sister ever pick or scratch at any of these areas? If so, that could explain at least some of what you're describing, and of course it won't get better unless she stops. Just a guess.
Good luck.
Dr. Rockoff