Welcome to the fun!
Tent: Check out something like a MLD Supermid with bug liner. About 3 pounds for the combination, inner is ~7.5 feet per side.
Sleeping Bags: For kids, check out the Western Mountaineering Tamarak, 19 ounces, $200, super compressible, last forever.
Stove: Yup, love the Caldera. They make systems for 2L pots that should work well for you. For the ultimate in weight savings, you might inquire about a Ti-Tri version... burn wood and save fuel weight...
Packs: I don't have kids, but I used to be one! You're right not to overload them, but at the same time they'll kinda enjoy hauling their part of the stuff... give one of them the tent stakes, another the pot, for example? But back to the pack, you might be able to pull off what I refer to as the 'tweener pack. Something light, though not necessarily ultra light. 70L or so. Maybe a GoLite Quest or an Exos 58 from mass market, a ULA Catalyst or something from cottage...