I would not encumber young kids with anything more than maybe some water and food, and keep them close enough that the chance of separation is as low as possible. Unless you take your kids out and hike them around hard so that they are used to it, all they will end up doing is whining about the load until you get tired of it and decide to hod their stuff for them anyways. Also, by keeping the supplies/equipment with you, you reduce the chance of them wanting to waste/lose items.

As for pets, the only time I would bring a pet with me is for wholly practical purposes. If the thing can't help me acquire food or provide some extra measure of security or hod stuff for me, then the only other reason to tote an animal is as a potential foodsource.

Untrained animals and untrained children can be a huge debtriment/liability in a bug out situation. Then there's always the "Can't get to them in time" scenario, which has cost me enough sleep in my life already.

I have discovered that it is much easier for me to have my family safely tucked away in some secure suburban setting while I am off facing a harsh environment than to have them with me and in harm's way. Life perspective is very much different through the spectacles I am wearing now.