Mice can chew through almost anything, so a tiny crack can be the beginning of a hole big enough for them to enter. Going under your trailer to check for possible entrances is a good idea. I suggest, if possible, working at night or having the trailer in a dark place and using a very bright light inside the trailer. Best to have a someone inside who can open the storage areas and shine the light around the pipes, wiring, edges, etc. This technique can be used to check the compartments from the outside too.
We avoid poison, not only because the mouse could die inside but because if they die outside, they can be eaten by a pet or another animal. We live in an old home in the country and were plagued by mice until a couple of remodels solved the problem. We used Havahart traps and released the little critters far, far away. If you find no entry places at all, I mean no light is visible even through the smallest crack, that would mean the mice (dead or alive) are still inside your trailer. If you don't find any, they must have found a way out.
On our last trip of the year, a mouse got into the car. The dog sleeps and sometimes eats in the car so the doors are occasionally left open for a short time. The mystery of how your mice entered may be that they got in the last time you used your trailer. The fact that you found no evidence when the trailer was emptied and cleaned may mean there was only one mouse (pregnant?) that had not been there for long.
So far as keeping them out, caulking cracks and using fine steel wool (nothing with soap in it) for larger spaces should work. And most important, plugging the electric cord hole and having the cord taut so it doesn't get close to the ground works for us. BTW, I used ammonia solution (diluted) to clean most surfaces. Perhaps (?) that would work on the carpet too, maybe using a sponge or spray.