ASD, Eating Disorders and puberty

Hi,  I'm new here and to knowingly mothering a daughter with ASD.  My 16 year old daughter has just been discharged from a CAHMS tier 4 inpatient unit after a 14 month battle.  She was admitted due to her being diagnosed with severe anorexia but as her brain became more nourished it was clear to her psychologist that there was something going on in addition to anorexia and was subsequently assessed and diagnosed with high functioning ASD.  My daughter has struggled to shake off the anorexic thoughts and hasn't really engaged with any of the therapy provided.

Although she has taken the diagnosis well I don't think she really believes it to be correct.  She has just started college but is struggling due to the social anxiety/expectations and is already getting stressed regarding homework and timescales (which we believe led to her anorexia has she approached her GCSE''s).  This is making my daughter's anorexia worse and she is very close to being readmitted to CAHMS tier 4.

I'm desperate to help my daughter beat anorexia but don't think she will until she gets help/support for her low self esteem and mental health issues arising as a result of her late diagnosis of ASD.   The current family based therapy for anorexia does not work with my daughter.  Does anyone have any experience of ASD and anorexia and any treatment or suggestions that might help shake the rigid thinking.  I can't see anything positive on the horizon for her at the moment and don't really know where to turn to as all this is so new to me.  Thanks.