I’d love to discuss this some more
I have a background in materials and engineering. I haven’t done the trip but I spend time outdoors and walk some good distances with my little one, and often thought about the issue.
I would probably add/change (not necessarily for children though):
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cordage (e.g. paracord, even dental floss or duct tape can vastly improve temporary shelter, duct tape or other adhesive doubles as band aid), some shock cord (elastic) can also be very helpful.
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alcohol for desinfection (e.g. the hand wash gel type)
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another space blanket (very little weight high utility especially with some how-to, also good as toy), with your background you might find a way to rig it into a jerven bag like thing.
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pieces of sleeping pads, probably sized to be large enough to sit on when folded once, becomes more useful with cordage.
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Power for phones: booster for charging from small batteries, buck (alternative) for charging from car battery (1 has enough for 200 phone charges), should probably be ruggedized e.g. by dipping in candle wax.
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for kids a hand warmer can help out a lot in increment weather (single use)
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at temporary camps a rugged bluetooth speaker could really help the kids unwind
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maybe replace the gloves by more socks that can be worn on the hands as well
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I would recommend 2 caps (beanies that go over the ear) if you have enough
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some water bottles have a special kid friendly openings but attach to regular bottles.
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In terms of shoes I think slightly oversize croc style (rooms for woolen socks, or maybe inner soles?) are the best minimum stress options.
I am mulling over a system that lets you improvise a “suitcase on wheels” with sticks and cordage. The parts you neet to have of course are the wheels (ideally in pairs, anything from skateboard to scooter will work - they all have 6 mm inner diameter). So this or this would be needed on site. But the two screws that “go in” would have to be replaced by something like 5mm (I think) threaded rod, which would become part of the axle.