Good for you. I want to take a "can do" attitude here, but beefy does have a point - it is going to be a struggle walking much of a distance until the children can carry a reasonable share of the equipment. It depends a bit on how old your middle children are - the 11 year old should be able to carry their own sleeping bag, mat and clothes, but younger than 6 or 7 they probably won't be making a significant contribution to portage. We've only really started backpacking as a family since most of our kids (we have three) have reached their teens. However, on the plus side you can get some "economies of scale". For example, we've recently started using a Luxe Octopeak lightweight teepee style tent. Since this squeezes all five of us in, and pitches with walking poles, its 3kg weight averages out as only 600g per person, which is a tent weight you'd struggle to reach as a single backpacker.
Likewise stove and cooking equipment doesn't necessarily increase in weight in proportion to the number using it. Unfortunately the truly lightweight camping cooksets are sized for one or two people and just aren't big enough for a family. My family cooking top tip would be a Tefal oven cake-tin as a frying pan - weighs 200g for a 27cm "frying pan" with a high quality non stick surface. And take a small gas stove - meths, although lightweight, can struggle to have the "oomph" to cook for a big family (though a good compromise which we use is a gas stove for cooking and a little tin can meths stove for brews en route, which supplements the cooking options when camped).
Children seem to sleep suprisingly warm and with little cushioning - they'll still need insulation from the ground, but inexpensive and very light foam pads will probably be fine for sub-teenagers. My 17 year old daughter now insists on a neoair the same as us, and the younger two (14 and 11) are on self-inflating foam pads. Child size sleeping bags are available from several of the big names - Vango, Blacks etc - and while not particularly light for their size, and not given specific temperature ratings, we've found them quite adequate for temperatures down to probably just a few degrees.
Good luck, though - and let us know how you get on!