Just to add to Etienne's reply, we were relieved to find that appeal panels can and do take any arguments into account, including ones that are based on good old common sense! Our panel was very sympathetic to the sibling issue, the fact that different schools in the same authority applied different rules depending on whether or not they had foundation status, and the logistical nightmare of having children dotted around various locations!
If you present your case as clearly and sensibly as you can, having researched all the possible options (e.g. bus timetables showing lack of alternative transport, breakdown times/locations of dropoffs and pickups for the various children etc.) and - if possible - some evidence that your DH will be working away, then hopefully your panel will be as sympathetic and as reasonable as ours was!
Obviously there are no guarantees as the school's case might still be stronger, but if you present all the information at least you'll have done all you can.