Honestly, Mice typically don't come into houses unless they smell food there. And Mice will not stay in a house that doesn't have food available.
So, sure you must find and block off their entry point, but you also must clean up and dispose of anything they may want to eat from your outdoor kitchen. Anything you keep out there must be kept in sealable glass or metal containers they cannot chew their way into. All food scraps must be cleaned up.
Then check out the gaskets around that drop door on your outdoor kitchen and make sure they are tight and the door is latched tightly all of the time except when it is in use.
And one more thing you need to consider is that they may be getting into your trailer and going from the inside to your outdoor kitchen.