NC for this as I have been following this thread as someone who has recovered (genuinely) from anorexia (12 years ago).
Firstly - you are all doing an amazing job... what you are going through as mothers, wives, partners, daughters, friends (because you have a life outside of caring for your loved one) is incredibly tough.
However, I did feel compelled to write because I can, with certainty, say that it is not as simple as just eating more and it disappears for every child. The previous poster was correct about the psychology side. Treatment focuses on weight to begin with because it is true that it is hard for someone to focus when starved as their brain is not functioning optimally. It is also because they are at serious physical risk. BUT - and this is crucial - for many sufferers, the illness is triggered by a trauma / worry / inherent feeling of not feeling good enough. I was in inpatient for 6 months and we all had different traumas. There are, of course, like some of your DDs who don't, but it did make me despair to see that it was held up as the only option - just eat and recover. Please do not believe that because that works for one child, it will work for another. That is a fast track to relapse if your DD (or DS) has underlying psychological issues.
I say this from someone who has felt the immense isolation, pain and suffering of anorexia. I was incredibly fortunate that, after relapsing, the underlying trauma was identified and I received the correct support. I would urge you to all show compassion to your DDs and be inquisitive... yes they are ill, but they are still human beings who are suffering. They need to be listened to (when thinking rationally and not having an ED fuelled melt down) and they need to learn to trust. Ultimately, many got unwell because they felt they had to turn to anorexia to numb whatever pain they were in.
I would recommend that those of you with older teens purchase a copy of the MANTRA book - it will help you and your DDs.