Broken, this young girl has been hospitalised three times. She was referred to the unit after the third hospitalisation. She could not go upstairs without collapsing. She had a dangerously low BMI and was worried about calories in water and toothpaste. She had lost touch with reality and was consumed by the ED in other words, and it had almost killed her, physically.
For starters wrt working at her A level coursework, she is probably in no condition to work meaningfully until she has recovered sufficiently in the physical sense, because the brain is affected by starvation. What the GCSE courses accomplish is group identity, first and foremost. Nobody is really worried that the patients might fall behind or fail their GCSEs because the spend time in the unit. The (limited?) courses available are there to enhance the communal spirit, to send the message that the patients are all in it together.
Secondly, wrt feeling special or unique, the DD needs to understand that she is not different from everyone else in the unit in any respect, including the social anxiety, and efforts on her part to dodge the group therapy can be seen as a way of expressing denial that she needs to be in the unit. It's a way of saying she doesn't really belong there. Allowing her any activity or to miss any activity that the others must do is a way of enabling her perception that she is different, which is a skewed perception resulting from the ED think and the physical effects of the ED on the functioning of the brain.
Wrt what the OP has been told about social anxiety affecting most of the patients - this is not dismissing it as no big deal. It is an effort by the unit to convey to the parent that her DD needs to accept her sameness and so does the OP. Doing well in individual therapy while not engaging with the group therapy is analogous to the eating situation at home, where the OP is delighted to see a good deal of a plateful of food eaten while at the unit a calorific drink is presented when food is refused. As with the calorific drink, the unit also wants her to engage with the group therapy, which the other patients must also do in spite of social anxiety.
Protocols for dealing with ED are well recognised. For the most part the wheel does not need to be reinvented for each patient. Part of the path towards recovery involves chipping away at beliefs the patient may have about herself and this may involve a belief in her inability to cope with a group therapy regime, or social anxiety in general.
Broken, I am not judging the DD here. Her brain is malfunctioning as a result of inadequate calorific intake and her perceptions are skewed. She cannot see how important it is for her to accept that she needs to change what she has been thinking and doing. It is very hard to give up mental habits that have been present for years, that have been exacerbated by the physical effects of calorie deprivation.
I am not judging the OP either - I would hazard a guess that she would give anything to see her DD whole again and free of the ED. Sometimes you have to stand back and let the child make the long journey back towards health on her own.