I have the same challenge and to further complicate things I have three kids with nut allergies.
We do a lot of fruit, berries with homemade whipped cream (no sugar), apples, grapes, etc... Cheese is also a good snack that fills them up and they all enjoy, smoothies as well. I have one that will snack on raw veggies but the other two won't. For lunches we will do turkey roll-ups with cream cheese and thinly sliced cucumbers but there are days where we have to revert back to a good old sandwich. I figure that keeping them 75% primal on average for a week, and staying away from processed foods, that we are doing pretty good.