There is a saying that if you found 1 mouse there are 5 more... or something like that. We went to a state park once and after 2 nights we suddenly heard scurrying in the night. We learned later that all the campers around us were having the same problem. Having an invasion at a camping site was a first, and thankfully last, for us. We opened up nooks and crannies behind drawers, behind the inside furnace and water heater cover, in our outside kitchen, etc. I think we put out around 8 traps. We also put dryer sheets around anything touching the ground (tires, hose, electric, etc). We caught probably a dozen and it took 2 days to get rid of them. We were happy when we left!
Campgrounds can be VERY attractive to rodents! If you think about it.... people are constantly cooking outside, leaving trash bags on the ground in and around campsites, while eating - possibly droping morsels of food on the ground, (FHU) septic dumps at each campsite pets, visitors, kids, etc. Its a freaking FREE rodent smorgasboard!
We too had a similar experience where we picked up some "travelers" while camping and didnt know it till we got to our next campsite. Luckily, no damage but some chewed paper and droppings. Some well placed traps with quality bait (Roquefort blue cheese) and eviction notices where soon enforced!
The first way to combat it, is to try to avoid poorly (dirty/non-well kept/poor reviewed) ran campgrounds as much as possible. Also, if possible, dont choose campsites TO close to CG common areas (bathrooms, pavillions, play grounds, dog run pens, trash dumps, CG leach fields, tent camp areas, etc).
Once at your selected site, prep your site prior to setup (inspect for any food/trash/pet droppings on ground). Keep trash in a container until ready to dispose of, monitor your RV for any leaks, and be vigilant about cleanliness in and around your RV.
You can try to use peppermint oil sprays and other deterents (dryer sheets) outside, but, weather can mitigate those easily, and some have claimed it can attract rodents as well. We always setup sacrficial baited traps in our forward passthru and under our hutch (common entry places in our rig) while camping and storage. Past 5 or so years, been very successful. Good luck!