Take a kids wagon to bug-out?
Seriously, how far is a person going to bug-out with 2 adults having to carry food & supplies, push a wheel chair and have 2-kids ride in a wagon? And the kids will want to ride in the wagon, (having been a parent, I can guarantee this) so you need 2 wagons, backpacks for food and supplies.
If you go with bicycles with a trailer on each one, who’s going to push the wheel chair? A battery powered one will run out of power in a short time, you need a manual one if you plan on walking out of any given situation and it’s any distance to your target area.
The adults will have to pull 2-wagons, have heavy backpacks on and push a wheelchair. After 15-min of this it’s going to cause you to want to go home and wait and hope for the Calvary to come rescue you.
You can’t put all you need for 5-people in 2 backpacks and a wagon. It’s not realistic to think this would work.
Again bugging out in this situation is going to involve an auto, and hopefully one with a roof rack. Even folded up a wheel chair can fill up the trunk of a car, that’s why you need a roof rack. And extra gas cans full of gasoline.
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You can run, but you'll only die tired.