We have 3 dogs, 2 basset hounds and a Boxer. We don't have a motorhome and they don't get carsick so I can't speak to that part of things. We also do not full time, just vacation.
I would suggest before heading out on a long trip with them is go somewhere local for a few days to see how they do. Every dog is different. Our oldest basset hound is happy as a clam as long as he's with us, so he's a great camping dog, except he's 12 with back problems, he can't make it up and down the steps of our 5th wheel, so we lift him up and down. Our younger basset hound is not a good camper. She gets nervous in new places and isn't the friendliest with strangers/new dogs so she barks and won't potty for a couple days. Our Boxer is a good girl but still a puppy (not quite 2), but too friendly and loves to run, so we have to keep a close eye on her. This year we tried one weekend trip with all 3 and decided it was a terrible idea LOL. We just took the boxer on the other trips this summer and left the bassets at home.
We haven't run into issues with pet limits, but we also tend to stick with state or county campgrounds and none of our dogs are on restricted breed lists.
I might suggest getting them an outdoor pen that way they can spend time outside off leash if you are confident they won't try to knock it over. We use a metal one that's about 4 feet tall. It has stakes to secure it to the ground and I throw a blanket over the top if it's hot out.