You need to figure out how they are getting in and make it harder. A mouse can get in through a hole the size of the end of your little finger. Use steel wool, or metal scrubbing pads. Exterminators can sell you copper mesh, about 6" wide by however many feet you want. I paid a buck a foot and 5 or 10 bucks will do you for a long time. This works better than steel wool, because it compresses into the hole better. Follow that with some of that expanding spray foam. Get the rodent resistant kind. Check where your shore line cable comes into your RV. If you aren't careful, that's like putting out a red carpet for them. Keep food sealed up as much as you can to try to avoid the odours attracting them. We never cook in our RV, not because of mice, that's just the way we camp, we like to cook outside, but in 40 years, we have (knock on wood) never had a mouse in the RV and I think not having the cooking odours might have something to do with that. Be very careful about bringing in boxes or containers that have been sitting outside into your RV. You can being in a mouse with it.
All these things are ways to keep them out. If you already have them, the only way to get rid of them is to trap, or poison them. Once they are in, they make babies and the problem starts to compound itself. Live traps if killing them is an issue, but I think if you ever turned down the sheets before going to bed and found a fresh litter of baby mice in your bed, you would be less squeamish. That happened to my niece last summer while we were camping with her. Yuck. Poison as a last resort for obvious reasons.
Talk to an exterminator. They can be very helpful and they have seen it all.