Wanderingfree - Your second paragraph encapsulates exactly what I was getting at. Unless a child is so far away from the average that this could be classed as a special need, there is not much to be gained from arguing that they 'need' a certain school because they are bright, gifted or talented. Otherwise, all schools are expected to cater for a range of needs.
Your second question is a little outside my experience because, as I said, all primary schools locally are for 4 to 11 so the issue of linked appeals for infants and juniors doesn't arise, although there are occassionally appeals for siblings at the same school. That said, the LEA do try their utmost to schedule all appeals for the same school with the same panel (usually on the same day) so there is consistency. That doesn't necessarily mean, though, that appeals for siblings will stand or fall together. I suspect most do, simply because very often the same arguments will apply to each sibling, but I suppose it remains possible that if the siblings' circumstances or needs are very different, it might be easier to demonstrate prejudice to one sibling than the other and so one appeal might succeed while the other fails. It certainly isn't the case that the panel for the second appeal is obliged to reach the same decision as the panel in the first appeal, as each must be decided on its own merits.
I understand your apprehension about the school run, but (as discussed above) logistical difficulties with the school run are never going to swing an appeal. Any panel would be sympathetic, but they lack the power to admit a child (especially in an infant class size case) on such grounds. It's conceivable that you could have two children at two schools for a while; our LEA's stock advice to parents in that situation is to share the school run with a neighbour or use a childminder or before and after-school club. Nobody suggests that this is ideal!
In all of this, I do need to emphasise that these are my views, drawn from my training and experience, but I don't want to deter you or anybody else from presenting the appeal in whatever way you choose. I'm also hoping that Admission and Prh47bridge may pitch in to this thread, because they sometimes have a slightly different take on things.
Finally, I'm nosey. Are you willing to PM me with where you live? I'm intrigued.