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.
I have. Child has an Isla.
It seems to be the market leader and it sounds like the seatpost ones aren't great.
Not cheap though.
@Mat-CR started
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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.