The disease is Munchausen by proxy.
There is not enough publically available information in this case to be able to determine if the child is really ill, or if she is a victim of Munchausen by proxy.
Usually, it is the mother who inflicts Munchausen by proxy, while the father, who is completely unaware of what is going on, believes the child to be genuinely ill.
The only drawback to that idea is the child improves under hospital care...in this case that has not happened.
It’s obviously not Munchausen by proxy. The daughter has been away from the parents for some time now. If her symptoms were inflicted by her mother she would be cured by now. Looking at her pictures she appears markedly worse.
If that were it, the girl would be getting better, not worse, since she is no longer with her mother.
As I read a little more about this story I got a little thought in the back of my mind wondering if this might be the case.
I read something last week (The Blaze or somewhere, I can't find it right now) that all their children seem to have a bunch of obscure medical issues. This does not mean they are not true but I now have a few doubts.