I agree with Prh47bridge.
There are several issues here.
What do the school's admissions criteria say about how distance to school will be measured? Do they specify which gate will be the fixed point from which all measurements will be taken? Are you suggesting that they have used a different fixed point for you than they have for all the other applicants? If so that would obviously be an error, but it isn't clear from what you say that it is an error which has deprived your child of a place (which is what the panel will be looking for) - it would depend on whether the new (shorter) measurement would put you inside the distance at which the last place was awarded. By the sound of it, you are a long way out of catchment and (perhaps) a long way past the distance at which the last place was awarded.
The situation is different if you are arguing that the fixed point, although it has been used for all applicants including you, should be changed to another one. The panel may or may not be open to that argument. They may take the view that they are there to scrutinise the admissions criteria as they stand and can't take any position on whether the fixed point should be shifted from one gate to the other. But, as prh47bridge says, if they do agree that measurements should be taken from the other gate, they may decide to deal with this by making a recommendation to the LEA (and leaving it in their hands). Or they may ask for all measurements to be redone. What they almost certainly won't do is take a measurement for you from one gate and compare it with measurements for all the other applicants taken from the other, because that would not be a fair comparison.
I can see the difficulty you are in - and I am sure the LEA and the panel will too - but the LEA's position will be that the admissions criteria have been designed to give priority to local children, ie those living in catchment. That is why out of catchment children - and their eventual siblings - are low on the admissions priorities. They will say that you (presumably) went into this with your eyes open when you accepted the first school place for your oldest child.
Given that this will be an infant class size appeal, you will need to produce more compelling evidence than saying it will be inconvenient to have your children in two schools. That much is obvious, but it isn't (unless you get a very sympathetic panel which is willing to stick its neck out for you) enough to win an infant class size appeal.
Rejecting the place you were offered will not boost your chance of winning the appeal (possibly the opposite, if the panel feel you are attempting to pressurise them). What have you done to find your child a school place? As a sibling, your child will presumably be quite high on the waiting list but you need a fallback plan for if you lose the appeal and don't get a place from the waiting list by the time your child is 5.