I'd suggest cut up raw veggies for one thing- you can pre-cut some and put them in ziplocs or tupperware containers. Cut them up fresh daily in the campsite too- take lots of carrots, snap peas, celery, and if your kids eat avocados take them too and cut open as needed. Apples, bananas, pears etc. are all great camping foods too.
Maybe bring some almond butter to fill the celery sicks with, or to spread on cucumbers. You are going to be limited somewhat by what your kids will actually eat at home. As @gilliebean suggested, hard-boiled eggs are perfect snack foods.
And @tattooedchef's comment about prepared soups/stews is great too- when we traveled from Mexico to the US I used frozen containers of soup and stew as ice packs for the cooler, and then ate them as they thawed.
One of my favorite appetizers on our road trip was the tuna sashimi with wasabi and a bit of soy sauce (bad!). Kids might not agree. Perhaps canned fish packed in water would come in handy if they eat fish. Find them the Paleo-friendliest wieners you can find too- that can be in their 20%. After all, it is a holiday.
As far as meat goes, I hope you have some kind of camp stove to use since raw meat is not too popular with most kids. If you pack some frozen meat it acts as ice in the cooler until you need it. Easy ones are steaks, kebabs, chops, and road-kill chickens (flattened out!).
Since we travel in a dinky 13 ft.Boler I usually cook up at least a pound of bacon before we leave and wrap it in paper towel in a tupperware container- it is simple to just warm up in the morning when we are frying eggs.
Have a good trip!