What you can do for children really depends on the age. Under a certain age, very young, the odds are you will be carrying them let alone any expectation of them carrying a pack. As they get older, you simply size the pack for their capability.
There are two basic approaches to family bugouts. One is each as independent systems in case you are separated. The other is expedition style packing.
Since I do not accept the option of separation, basically that would stop everything till we are united, I endorse the expedition approach. Losses in a family simply are not acceptable.
An expedition approach is to share the weight of common gear such as a tent, cookware, food, stove, fuel, etc. Its very similar approach to say an expedition to climb a mountain. This allows you to carry more gear due to less duplication.
Quite frankly with small children, I wouldn't plan on them carrying a single thing. Just by length of their legs, they'll be doing great if they just keep up.
Tj