I'd build a bigger version of the SB Cruiser trike,
https://endless-sphere.com/forums/viewt ... =2&t=67833
with a expandable "camping" trailer that could carry the dogs, their food and stuff, and my food and stuff, and tools/parts to fix critical things that might break on the road, as well as a generator and gas to run it (as much as I hate that, it might be necessary between cities and charges).
Of course, that all would depend on me winning the lottery to free me from the need to work for a living.
If I did, I'd also build the trike and trailer from all-new materials actually intended for their purpose, so I could be sure of their dependability (I've had some issues iwth some of the recycled materials used over the years not being up to the more stressful purposes I used them for, like this recent example:
https://endless-sphere.com/forums/viewt ... 5#p1339930
so I'd want to use new stuff I could count on to prevent that).
Solar charging from panels on the top of the trike and trailer would be great but impractical; I couldn't carry enough to make up even a small portion of the power I'd have to use to haul this around. :/ I'd probably build some in anyway, but they'd just be a kind of backup / trickle charging vs what I'd rely on to stay charged.