Holy dead thread Batman, at least it's relavent. I was thinking about using a push trailer as opposed to actually motoring the bike, it seems like a somewhat funky twist and a somewhat better way to add some power being that it's basically a trailer and can be separated from the actual bike easier than a weighty and well bolted engine. I'm still not even sure if it's legally still a bicycle with a gas motor propelling a trailer wheel. What's really nice is a power source placed so far back and with a pivot in the middle it really encourages you not to use it at high speed, things like that get kinda hairy when moving quickly enough.
Kind of imagine driving in reverse as fast as your car would let you, but worse, at least in terms of handling.
I'm wondering if it's better to use a universal type joint or use a true pivot like a tow ball, my concern is that leaning may not cause a trailer to lean since I would like to use a single wheel trailer if I decide on this route, a true pivot let's the pusher lean out of the same angle that the frame is holding, meanwhile the universal type joint attempts to preserve the angle that the bike frame holds but allows the 2 angles needed for bumps, verticals, and turns which are the horizontal motions. If you use a 2 wheeled trailer you are basically obligated to use that true ball pivot or spring type alternative joint to allow a standard 2 wheel bike to lean left or right.
I've also contemplated a side trailer with a motor but that is a bit more complicated and better reserved for a literal doggy bag to house a friendly companion, better yet a push trailer puts the noise even farther away if a side cart came to be.
I saw some pull behinds for bicycles, you have a child ride it, I would think that removing the seat and handlebars would be a decent first step in attaching a motor to it, then it's just a tank and some extra long cables but otherwise a half decent bike could be attached without fear of really wrecking the thing. I've seen a couple schwinn spoilers for sale, those are just gorgeous bikes, I would imagine a tasteful trailer would be a fair addition to a bike like that without really disrupting the bike itself (which is really nice looking, expensive, and rare.)