We did a fair bit of traveling with our 4 hens over the past several months and I quickly found it necessary to make individual boxes with doors, inside their coop (coop was also inside a covered trailer) as we noticed they were tumbling about a bit when simply interred inside the coop while on the road. (A chicken-cam is another must have imo) We also figured winds and debris might not be ideal, thus the whole idea of putting the coop inside a covered trailer, towed behind the motorhome.
Fortunately the trailer, which is used to haul a small pickup and the "toys" was big enough to put the 8x4x6 foot coop across the front and the hens twigged onto the location as home really quick with some practice. Didn't matter where we went, they knew where home was. A large screen tent as a run was really handy too for short stays, with some rolled up semi- rigid wire for longer visits.
Our experience was that they seemed to travel better during the day, or at least with the lights on. Night or dark travel always lead to a failure to disembark their passengers (eggs) the following morning and we were very much on guard for egg-binding etc. I would recommend a few dry runs first, to shake out any issues and get them accustomed to traveling. Ours proved to be very hardy and trouble-free travellers, but some common sense goes a long way to guaranteeing safety and good health.
I possess little common sense, but The Ministry of War and Finance has buckets. I just had to drive the whole shebang. And build it. And clean it. And feed them. And pay for everything. Sigh...