I'd just carry a socket wrench to remove your kid's front wheel. Get a $10 truckbed fork mount, a $20 rear rack, attach fork mount to rack.

Remove kid's front wheel (bring an extension if he's got pegs), lock fork into fork mount, toe-strap kid's front wheel somewhere.

Of course, with a cargo bike or trailer, you can haul a few other things than with this setup on non-school days, but they're way heavier and likely way more expensive...