If you don't have a washer and dryer area, you can put a litter box under the couch (sometimes). Ours goes under the couch and the cats don't have any problems. I don't like putting them in the shower.......no matter what we do about it, one of our cats will kick the litter out. I worry about it going down the drain. And yes, I've lined the shower with papers. We shower every morning in our rig (that's why we bought it!!!!).....and hated the work involved with removing and replacing the litter box.
BTW -- start by taking the cats out to the rig and sitting with them for an hour or more. Keep increasing the time, then after a week, take them for a short ride......then increase that. To just toss older cats in a rig and driving off will scare the bejeebers out of them!