This is what I said on the other thread. PRH also posted there.
Hello Brooke.
First things first. They don't set aside any places for appeals, so if your child is admitted it will be as an 'extra'. (I can say more about that, if you wish).
I'm confused by your description. You say you've appealed twice already - do you mean for this school? You can usually only appeal once a year for the same school.
You say that 40 children have been admitted. Does that mean that the school's PAN (which you can find in its brochure) is 40? How are the classes arranged? Is it 2 x 20?
Class sizes in key stage 1 are limited by law to 30 with one teacher. Where schools have 30 children in each infants' class, appeals are heard under infant class size rules. These mean that the panel can only admit the child if there has been a serious mistake in applying the admissions criteria which means that the child lost out.
But if the classes are smaller than 30, those rules don't apply. Instead you would have to show that the prejudice (disadvantage) to your child in not going to that school is greater than the prejudice to the school in having to take another child.
What does the letter from your HV say? You don't have to repeat it all here, but the panel will be looking for evidence that the school you are appealing for is the best one for your child. To be frank, though, I'm not sure how much weight the panel can give to a letter which is about your needs rather than your child's - that's why you need a letter which relates to your child, not only to you. To help you, the letter should give reasons for your child to go to your preferred school, not reasons not to go to the one you've been allocated, IYSWIM.
On the day, the hearing will start with the school/LEA stating why your child wasn't admitted. You can then ask questions. Then you get an opportunity to state why you think your child should be admitted, and the person from the LEA will ask you any questions. The panel should try to put you at your ease and make sure you've had an opportunity to put your views across.
If you give us more information, we may be able to offer more suggestions.