Look at everything the school can offer her, she needs stability, good pastoral care and a local friend base now she is to be long term fostered.
Look at clubs and other things within the schools ethos that will support your dfd and help her to settle and develop. Identify any clubs that this school offers that aren't offered by any other local schools and find out if they are of particular benefit to dfd (like aa athletics club if she is a strong athlete, music club/lessons if she is a musician), does the school have any specialist support in place for children who have had difficult starts in life or have suffered loss like an in school councillor. It is things like this that can win you an appeal as you can show why this school, and only this school is right for dfd.
Stay away from anything about childcare, transport or academics, these will not be able to be taken into account by the panel as parents are expected to deal with childcare and transport issues and all schools are expected to offer the same academic levels (even if we know in reality this it's not true, they have to see all schools as equal in this respect)
You are appealing for this school not against her current or any other school so do not rubbish or criticise her current or any other school (this can but the back up the panel, you have no idea if a pannelmamber has a child at one of these other schools!). Stick to reasons why this school is right for dfd and only this school.
Find out how big the class rooms are, have any other year groups in the past gone above 30 (I bet they have) and if so did this negatively effect the results or the school in any way.
When you put in your appeal you will receive paperwork that will state the schools case against admission, you can then use this to build your case, For example, if they say that public areas of the school will be over crowded and dangerous ask if there have ever been any accidents as a result of over crowding in the hall ways.
The school have to give you any reasonable information you ask for that will help you build your case and that is how you will get most of the answer to the questions I have suggested. You will need to state a basic case when you put in the appeal paperwork but you can add to and expand on this afterwards but don't arrive at the hearing with any big its of new information as you may find they will adjourn the hearing to give everyone the chance to go through it.
If you can get statements from your dfd social worker supporting why this school would be the best for her and also if she has any medical needs or a councillor get them to write an supporting letter but make sure that they are in their own words, not '7fostermum tells me that this school will be best for dfd' but rather 'In my professional opinion dfd needs to go to X school because of Y and z'
As this is not an infant class size case (YR to Y2) and not bound by the legal class size of 30 you stand more chance of winning this appeal. I imagine that a panel would be very sympathetic to you but you must prove that the balance of prejudice means that by not going to this school your dfd will be more disadvantaged then the school would be by taking on another pupil in the class.
I hope I have made sense and sorry it is a really long post. I hope one (or more) of the MN admission experts will come along and give you some of their trademark excellent and clear advice. I wish you well with this, keep us informed and any questions please ask and hopefully somebody will be able to help. Don't be put off with the fact it is a church school and 'they make their own rules', yes they have their own admissions criteria but the panel must be independent and they still have to stick to the admissions code.