You are lucky because your wife is willing to come along. Mine was not, so with two of them I had to carry a lot of extra stuff. But since small kids are not going to hike long distances, it wasn't so bad.
When mine were 8 and younger I just had them bring their little day packs they used for school and put as much stuff as was comfortable for them and carried the rest myself. I did a couple trips with the boy when he was older and bought a small pack I knew he would soon out-grow.
Always hike on trails that I knew someone would be on it in case of an injury. Fortunately I never had to deal with it. Realistically, kids are resilient and it is more likely that an injury would occur to you. When they were really little, I would talk to a ranger and discuss our trip. If they are out in the area, they will keep a special look out for you. On one trip we were a little bit off the trail playing with Hot Wheels during a rest stop, when the boy was 5. The Ranger saw us and came over to make sure everything was okay.
Sleeping bags. I just let them use one of my bags. It was too big, but it worked. Usually I had to use a lighter bag with with additional insulation to keep me warm.
Tents - this was the big problem, being a tarp guy. With just the boy I would use a large tarp, in weather with just a chance of afternoon showers. With a greater chance of rain I used a Sierra Designs Flashlight with the girl, (predessor to the Clip Flashlight). With the boy or both of them I often used an Chouinard Pyramid.
Clothes - just let them bring an insulated jacket which was fairly heavy, but they could carry it in their pack, as I was the mule. If it got cold at night, we just retired early and kept warm in the bags.
Bugs just don't seem to bother our family much.
I like you idea of acclimating first. Plus you have a two-staged camping adventure.
With young children, I have found you need to let them bring some sort of toy or diversion. For my son it was Hot Wheels until he was about 7, then after that it was no longer an issue. For my daughter... well this is strange, she would never, ever use a campground toilet. Backpacking was a huge concern to me, and she lived to be able to use a cathole and get to burn the TP. Who would have guessed.
Start with really short trips, and work your way up. Do too much at first and they get turned off. My biggest problem with BPing with small kids was finding the time, and an interesting loop with little elevation gain. All the other things we not that big a problem. I would be hesitant to take a kid under 11 on a multiday trip with any sort of mileage over about 5 per day. But this would be dependent on the make-up of the kids.
Have fun, you are going to reap tremedouse benefit by connecting with your children.