I'm afraid you are right. It wasn't considered. In all but the most exceptional cases the panel will not consider child care issues. Almost every single case quotes child care issues so, if the panel accepted these arguments, almost 100% of appeals would be successful and there would be chaos.
You need to focus on the way forward and use the system to your benefit rather than complaining about it. The rules are the same for everyone. Anything the successful appelants said about child care issues will also have been ignored. It is possible to win appeals. You just need to focus on issues that allow the panel to admit your child to the school.
Given what you have said about the way this appeal was conducted, you may have grounds for referring the case to the Local Government Ombudsman. At best that will get you a further appeal with a different panel but that is still worth a try. I and others will be happy to help you with your submission to the LGO. It won't cost you anything and you won't lose anything by trying.
Even if the LGO doesn't recommend a further appeal, you are entitled to appeal again in the new academic year (i.e. September). However, a successful referral to the LGO will get you a second appeal rather more rapidly, although it may be September before the hearing takes place.
At a second appeal, regardless of whether it is ordered by the LGO or not, you are entitled to submit a completely different case if you want. As I've already said, I think it may be possible to construct a reasonable case around your daughter's condition and the physical problems it will cause her. That would be a much stronger case than talking about child care issues and possible bullying. Again, I and others will be happy to help you put together a better case, although obviously we can't guarantee that you will win.
You also need to think about plan B. It may be that you will get a place off the waiting list but that can't be guaranteed. What if your appeals fail and you don't get a place through the waiting list? Will you home educate throughout the secondary years? Or would you be better looking at other schools which have places and seeing if any of them are suitable for your daughter?