If you do go the travel-trailer coop route, prices are way up (sadly), but I picked up a
folding 4x8 aluminum trailer (assemble it yourself, one day project) from Northern Tool. The folding part is BS. First thing I did was disable it and bolt down some heavy PT plywood.
In retrospect, a
5x8 or
6x12 aluminum would have been MUCH wiser - but I tow it behind a Buick Sedan, not a vehicle famed for its tow capacity - for picking up materials at the building supply. Weight was a real concern. And, of course, it doesn't rust. and I'd buy, not build,
a tongue box for convenient storage and to stiffen up the front some. Great place to keep a bag of feed, some odds and ends, etc
I don't use my trailer as a mobile coop - but if I did, that's where I would start (that, and a truck!), based on what I've learned using my flatbed trailer.