Thanks for your question about your daughter. The people that I know who need to rest in bed for 2 days after going for a walk are suffering from fibromyalgia, chronic fatigue or ME, but this sounds much more than this to me, given her eating disorder and other symptoms.
I am going to recommend to you that you find out more information about a 'trauma' therapy called EMDR - Eye Movement Desensitisation and Re-Processing. This therapy is based on the theory that the subconscious mind picks up messages from highly emotional situations and these messages become stuck in the subconscious mind as beliefs about the world, or about ourself. These beliefs go unrecognised but often cause symptoms such anxiety and depression, and whatever other symptoms are relevant - for example fears and phobias, or eating disorders. These behaviours are always supportive of the beliefs, so for someone who fears 'I will die if I get on a plane' then the anxiety, etc. is triggered when the person is going on a plane - this can be extrapolated to other situations, such as seeing a plane on the news or hearing one go overhead. They may not recognise that these planes are triggering the anxiety.
I wonder whether your daughter interpreted some of her childhood environment in such a way that she is holding beliefs that are affecting her life in a major way. Often, these beliefs can be wrapped up in the need to be perfect, for example, 'If I can't do it perfectly, there's no point doing it at all' or something similar. It really isn't worth discussing this with your daughter as consciously she may be genuinely unaware what the beliefs may be or where they came from. Asking her about them may encourage her to deny that they are there. A therapist will simply allow her, through EMDR, to explore her subconscious mind and find out the true cause. The belief that she will never get better will certainly not be helping her, but is understandable, given her situation.
It is important to state that no-one is to blame for these subconscious beliefs - often children interpret something in their own mind that they hear without having the adult skills to understand them better. It isn't your daughter's fault and isn't something she can control, although consciously she is trying, it is wearing her out. The beliefs are irrational and need to be removed.
The therapy processes away the emotional baggage that we can carry from the past, that is linked to the memories - the memories can then drop back in time and are much less important. Often these memories are currently extremely vivid, able to recall colours, textures, voices, noises, smells, etc. (If they are good memories, this is great - recall the time you got married or brought your baby home and see how much detail you can recall - the highly emotional experience is etched in your subconscious mind, but because it is positive, it causes no harm). Normally, we process away anxiety through REM (Rapid Eye Movement) during the night, but when the memories are emotionally high, they aren't able to be processed away this way. The brain may try to process them at night and can cause nightmares and unsettled sleep.
In order to simulate REM, EMDR uses a bilateral stimulation of the body in some form - often tapping, lights, eye movements or gentle electrical impulses - which encourages the brain to process the negative 'stuff' away. It is often quicker than talking therapies because the subconscious mind is able to tap directly into the problem areas. However, if your daughter finds it difficult to 'go to' some of the memories, the therapist will help her to do so slowly and safely.
Try www.emdrassociation.co.uk for more information and local therapists to you. There are therapists who specialise in working with young adults - try and find someone who has worked with eating disorders before if you can, but don't worry if you can't be that specific in your choice of therapist.
I hope this makes sense. Please get back to me if you have more queries. Best Wishes, Sarah