Don't force your kids to clean their plates at every meal. If you don't allow them to randomly snack, you would be amazed at how well they eat during regular meals. If you know there is going to be a longer period of time than usual between meals, plan on a healthy snack somewhere in between. But remember, it's a snack, not a meal!
Try 1 or 2 rolled turkey slices, some carrots and cucumber spears and a closed handful of nuts.