I've been back to your previous thread and refreshed my memory. That thread suggests that it is probably your Y4 child that has been admitted. Is that correct?
Your biggest problem is that this school has a PAN of 35 but a capacity of only 204. That PAN is far too high compared to the capacity. The PAN should be 30. My quick thoughts for stage 1...
Make sure the panel are clear that there are 4 classes in infants and therefore this is not an infant class size case. Their current class arrangement allows them to have up to 40 children in each year in infants before they hit infant class size limits.
Point out that if every year is full to PAN the school will have 245 pupils, well over the official capacity of 204. If enough pupils apply to fill each year the school will have to go to that number. Therefore the school and LA have already accepted that the school can cope with 245 children regardless of the fact that this is well over the official capacity. It only has 226 at the moment (assuming your child is the only one admitted since your appeal) and is therefore well under the level it would be at if it was full to PAN.
The bulk of the LA's case last time round was pretty standard. Pointing to the Ofsted report which doesn't contain any suggestion of overcrowding as you did last time may be a good move. If you want to do that again it would be a good idea to submit a copy of this report as part of your evidence so that the panel members can read it before the hearing.
None of this conclusively proves that the school can take your children. What I would be trying to do here is move the panel away from thinking this school is ridiculously overcrowded because of the high PAN and instead get them thinking that the high PAN means the school must be able to cope with more pupils, otherwise why was it set so high.
It is also worth pointing out to the panel that the school currently has 37 in Y1 and is coping with this, so admitting your child to Y2 (which only has 35 at the moment) shouldn't cause any problems.
The other point to make, of course, is that you need to give reasons why your children need to go to this school. The fact they have a sibling there already is a good start but anything else you can come up with that suggests they need to be at this school will help to bolster your case. Concentrate on things like after school clubs and other facilities this school has which the allocated school does not.
There are no guarantees but, given that Y2 only has 35 children (assuming nothing has changed) I think you have a reasonable chance of winning that case. The appeal for your Y1 child may be more difficult to win because that year is already 2 over PAN. It is a shame there isn't a year with 38 children in it already! However, being optimistic the panel may take the view that they have to admit your Y2 child and that having two children there already means they ought to admit your Y1 child as well.
Good luck!