At least one parent can travel on with the other child and the other parent can stay behind and sort one lost passport out. That's way better than everyone staying behind and sorting four lost passports out.

Besides, I'd have each parent carry his/her own passport plus one child's passport. This way they go in groups so to say.

This comes from someone who accidentally threw away a paper ticket (in the time before internet) when emptying his coat pockets after a long trip.

Till