Storage of feed is in plastic trash cans - no problem there. When I feed chickens on ground, mice enjoy the free meals. Can't place traps or poison for fear of chickens finding it.
Chickens have free reign over land.
Heard that moth balls will keep mice away, but don't know effect on chickens. Anything will help. Set your mousetrap inside this with some bait like peanut butter on it. You can also set traps under boards leaning against walls where the hens can't get in. If necessary, you could hinge these boards so they won't be knocked down accidentally.