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I have a follow me. It is solid af, I really rate it. Great to be able to attach and detach the bike in a few seconds, means you can switch up between pulling them along and riding side by side over the course of a ride. Defs not cheap but they don’t really lose value too much, so you should be able to recoup a lot of the outlay. Admittedly that will be a fair few years down the line.
Have you looked at a Follow-me tandem attachment? Would seem to tick all the boxes above. Obviously assumes your child has an existing bike. Probably the smallest option in terms of storage, and provides some flexibility when out and about too.