Okay, so my coop and run are not completely mouse proof but that was our goal. We had lost 2 different flocks of chickens to minks and I did not want to lose any more. We started by excavating out 1 foot of dirt and then framed that area in landscape timbers. We moved in a used shed and placed it on top of 3 stacked timbers so the chickens would have access to an area under the coop. We placed metal siding as a base.
We covered the siding with 3 inches of 1 1/2 inch rock.
We put landscape fabric over the rock and covered the fabric with about 6 inches of sand.
We framed the run with 4x4 posts and attached a metal roof.
We moved a small portable coop into the middle of the run.
We used metal sheets (masons or stucco) to secure the coop. We used screws and large washers and attached them to the 4x4 posts.
The sheets were easier to work with then the hardware cloth. We did patch any areas that a mink (or mouse) could squeeze into with hardware cloth. We used a metal screen door.
This last winter I wrapped the North, East and West sides of the run in plastic and it stayed dry and warm. My chickens loved it. I added different perches in the run. The run has been completed a little over a year and I really can't think of anything I would change. I like having the sand base. I can go in and scoop poop every day and it stays very clean. We have raccoons and minks and have not had any more problems with them bothering the chickens. I leave the door open from the coop to the run 24/7. I let them out of the run into the yard only when I am out there.