We had a very similar problem this year except it was with squirrels. My son and I have solved it as follows.
The squirrel, after getting in the trailer, had eaten a hole right through the metal foil furnace duct. I replaced the furnace ducting with an all steel one from Lowes. If he ever gets in again, he will have some broken teeth if he tries to bite this! He also chewed a large hole around the kitchen gray tank vent so we patched that up with sheet aluminum.
I discovered he got in via a small crack between the trailer frame and the front cap. My son and I closed that up with some sheet aluminum from Lowes. Here is a view of the cap now looking up from underneath next to the A frame. We did both sides of the trailer.
After gaining access to the area between the outer and inner wall, the squirrel ate a 2.5 inch hole in the inner wall behind a kitchen drawer and use some of the insulation to fill the drawer full for a nest.
I took all the drawers home and cleaned them out very well and we patched the hole with another piece of aluminum.
After looking around, we found another place where the squirrel had used to enter the living space. He evidently travelled in the underbelly material and ate a hole in the rear hall closet where the black tank breather goes up through the trailer to the roof. We then patched that hole with another piece of aluminum sheet.
We then proceeded to make a squirrel trap using a 5 gal paint bucket, a piece of 1x4 about 4 feet long, and some waxed sunflower seeds. Pour the seeds into about 6 inches of water in the bucket, place the wood ramp on the side of the bucket and let it sit overnight. Place a few seeds on the ramp and leading up to it..
We caught 5 of the critters this way and have not had a single occurrence or problem with them since. By the way, our trailer sits in my sons family campground right in the middle of the woods so there are lots of critters around. They were evidently living in our woodpile.
Hope you have good luck getting rid of your mice. They and squirrels can do a great deal of damage to a RV and I have no sympathy for them.
Barney