You could also use Benefiber. It has no flavor or texture, and is made from something natural (a bean, I believe). Put it in their food every day.
It can be a food allergy. My children are allergic to pectin ( found in apples, apple juice all jelled food like Jello ,jelly beans, jelly etc. ) Mineral oil will help. A tiny bit in their drink or even on a spoon will make it a bit easier to go.