OK. Here goes ......
Fair Access is at the discretion of the Local Authority, and is really meant for vulnerable children without
a school place (or who would have to travel a wholly unreasonable distance to get to school).
Moreover, I don't think a parent could select which school is to be allocated, not least because the LA will need to spread the extra children around, so that no one school is required to take a disproportionate number.
I do think an appeal panel would be sympathetic if you mention that your daughter is a carer, but your best course of action is to focus on why the grammar school would be a good match for her.
See:http://www.elevenplusexams.co.uk/appeal ... -school#c2
Read the Q&As, especially section C (oversubscribed schools):http://www.elevenplusexams.co.uk/appeal ... bed-school
If you need more time to fill in your appeal form, see:http://www.elevenplusexams.co.uk/appeals/general#a7
If I put in the appeal form wrong grounds will I loose the case?
This time I want to make it right.
I wouldn't have thought so. They ought to ask questions, as I have done, to understand your circumstances and why you want a place at the school.
The offered school has specialism in sport which she is not into sport
Better to focus on what the school you want can offer.