The terrain a cart can handle is also determined by the width of its track and the size of the trail.

While my wife and I have hauled our kids around in a wagon, I wouldn't do it in a bug out situation only for the fact that I can't see them behind me.

A sling and a messenger type bag seems to work for us as they both go kind of cross body. The bag goes on the bottom, then the kid in a sling. Easier on the kids legs that way too versus with a backpack.

We went on a five mile or so hike where the 2 year old just didn't want to walk. My wife and I took turns carrying her. My wife used the sling and alternately had our daughter go on her back and I just carried her in front since I had the heavier pack. My wife's messenger bag did not interfere with carrying our daughter with the sling or on her back while I could only carry her in front.

With young kids, it will depend on them whether they want to go or not. On our earlier hike, the two year old trucked it uphill for about a mile to get to our destination. But after we rested and waited for the last mom and child to make it up, she got really tired and fell asleep and we had to carry her back down. The five year old is a trooper though and will slog through almost whereever we take her. The only time she will complain is toward the very end of a long hike where her feet might hurt. Then I will carry her for a quarter mile or half a mile and she can usually finish.

It really helps when your children are vocal about things that might bother them. It helps in figuring out how much we can do.

Oh, I also find that kids (and most adults too) need frequent enforced rest stops to rehydrate and maybe snack. Snacks are huge morale boosters for kids.