Cats can certainly travel well in a RV - especially in a motorhome where the owner is right there. We know of various friends who do it successfully. Now if you put them in a trailer which bounces around a lot, that may be a different story.
Here's an excellent blogger full-time RVer who travels in a motorhome with cats and a dog. She gives some nice articles on the pets. By the way, after 8 years (I believe) of full-timing they just sold the RV and last week moved to France! They plan to get another RV there.
https://wheelingit.us/category/pet-corner/