Thank you for everyone who is joining this topic, some really useful advice, I wish I started this thread before the hearing. :-)
Yes, I did submit the medical letters at the time of applying. Social/medical reasons were part of the admissions criteria, but below the Catholic church goer criterion. So basically, at the time of admissions, they only prioritised her within the non church goer category; and they filled all their places with weekly churchgoers. Next category is fortnightly church goers, so she is way down on the waiting list.
It is very unfair, especially that I personally know a number of families who are not Catholic, but went to church for a year and as soon as they got the offer letter they stopped going to church and will never go again.
The doctors' letters were done for the admissions and not for the appeal and I used the same letters for the appeals as they were already very detailed. I did add a lot of other information and I also got a letter from the organisation for this genetic disorder. Because at the time of admissions we did not know which school she'd be allocated, the doctors' letters do not compare the appeal school with the allocated school. However they do go into a lot of detail about why it was essential that she attended this particular school, being the nearest to her home, pastoral care, and what difficulties it would cause if she had to attend any other school. I then prepared a case that also compares the appeal school with the allocated school.
I don't know what more I could've done. Although I knew that the panel does not have to follow the admissions criteria, I wasn't sure how much the church going would affect the appeal. By the way, we had a letter from a priest to confirm that the family is Catholic, but this has hardly any weight unless you got the stamp every week from the church.
I've heard that for Catholic schools the panel members are part of the church so their impartiality is highly questionable.