The foil packages may not work well and leak over the stove. I've only done foil wrapped things on a fire where leaking doesn't matter. But maybe veggies and sweet potatoes wouldn't have much of a leakage problem, so it might be worth trying.

How about freezing the chicken and packing it in the cooler frozen?

Back when we tent camped we did a two cooler system. One cooler was rarely opened so it functioned better. The second cooler was for things we used all the time or didn't have to be as cold, like pop and veggies.

If you really get into camping I can't recommend enough a Cobb Cooker. It is a small charcoal cooker that uses very little charcoal (like only 8 pieces) and can be used to cook a wide variety of things. It isn't like a traditional grill at all. Unfortunately, they are kind of pricey. http://www.cobbamerica.com/