Basically the same way you do at home, only maybe scoop it a little more often because of the smaller space.
Some people have put the box in their basement with a door for entry from the living room. Others put it in the shower. We keep ours in the LR next to my chair with a tray on top to make it into an end table.
We put 2 litter boxes in the shower stall and try to pick it asap. Sometimes we are away from the trailer for several hours at a time, that is why we put out 2 boxes which has worked for us.
__________________
Allan, Jeanne and Katie the cat Full-timers from Alabama "07 -40' Phaeton & '08 Jeep Liberty
Our cat, Bumper, loves travelling and being on the motor home equally to a house. As to the litter, we found a box at Petsmart that is entered from the top. The "Bumpster" caught on quickly.
We recently changed litter to "World's Best Cat Litter". It is 100% natural, doesn't stick to feet and clumps. There is just no odor. It lasts longer and though a bit more expensive, costs less in the long run. An other advantage is it weighs less. (Also available at Petsmart.)
We agree, it is the World's Best Cat Litter. Bumper did not get a vote, but seeminly likes it better. Hey, it works!
__________________
Ethel & Charles Henry, Itasca Horizon DP/Honda Element Toad Traveling with our furry-snouted, four-legged children.
"Each of us must take part in making this a better world for all people."
We have two same as you our rig came with a washer dryer prep (meaning a large enough closet with wiring and such but no washer dryer unit). Now I don't mind doing laundry at the campground laundry facilities so we use that closet for the cats. Their litter box down below and the litter on a shelf above.
We did get a rabbit pan (TSC has these) that was the right size to fill the closet in case of spills and that works well. Catches any litter they might toss about.
We don't care for the litter box in the shower idea as the Brideandjoy prefers to taker her showers in the fifthwheel and doesn't want to have to move the box around.
We pretty much use the same litter we used to use at home (Tidy Cat multi cat) and we do scoop twice a day instead of once a day like we did in the house.