There are livestock trailers with living quarters for humans. I've seen them often in municipal and country RV parks in this part of the country.
Another option, pulling larger trailers, is a "toter home" on the back of a Class 5 to Class 8 tractor. I see these pulling larger horse vans and cattle trucks, probably a lot more trailer than you would need for sheep, goats, alpaca, etc.
Not so much RVing, as these are usually carrying working animals, for professional or commercial use, and as such they are also not pets. Working horses for round-up, rodeo, racing; dogs for competition and hunting; show livestock on the state and county fair circuits.
I think toting around livestock will limit the places you are welcome to stay, more so than a couple of pets, even large ones.