I hear ya about opening the gate. I think it would be cheaper and easier to do the apron idea, but bury it a few inches deep. The description I read to put the wire in concrete seems like a lot of work to me, not to mention the added expense of the concrete. Also, maybe you'd only have to bury the apron in just the part to let the gate open. (Not sure that last sentence made sense).
Dave
Yes, that does make sense. We'll have to mess around out there and see what we can come up with. Fortunately, we're building on the grass, and we plan to move everything into place, so we can continue working on the run while we try to figure out what to do with the ground. My kids will have to walk their bikes through a thin area between the run and the house, we don't want any scratched up legs or popped tires.
We have ours (hardware cloth on the pnes) buried 12" in the dirt and the mink went right under it.
So we dug the dirt back up & poured concrete in it, dry, easy to do with the shovel...then sprinkled water on it & covered it back up the next day with the dirt.
My husband doesn't think we have mink here, but who knows. We do have a raccoon and opossum problem. We frequently see dead opossums in our neighborhood streets. Do opossums dig, anyone know?
Chickielady, I think that's similar to what my husband was talking about doing. My SIL gave us a huge roll of 1" chicken wire that had been left at her home by previous owners, which we are not using on the run or coop. We have 1/2" hardware cloth for the run and 1/4" hardware cloth for the coop. He was planning on cutting it to size, then putting a thin coat (1/2") of concrete mix over the top. The wire would be the predator proofing and the concrete would keep the chickens from hurting their feet as they scratched and dug. He planned to fill the floor back in with screened dirt and whatever ground cover we end up choosing.
Fortunately, digging out the area won't be too difficult. It's more a matter of smoothing it out. Whatever we choose, ground work has to be done. There's a significant hole in the area already (which is what gave my husband the idea). With our children's blessing, we reclaimed our children's digging area for the coop/run. They actually had the area pretty well dug down because they were trying to dig to the other side of the world. 
Hatched April 12, 2012 - Drama, a Light Brahma; Caunnie, an Easter Egger; and Rhodie, a Rhode Island Red
Hatched October 14, 2012 - Latte, a mixed pullet - a.k.a. a "Fudgelet"
Hatched December 9, 2012 - Snow and Blackie, Olive Egger pullets and Penny, a Black Copper Marans
Hatched April 12, 2012 - Drama, a Light Brahma; Caunnie, an Easter Egger; and Rhodie, a Rhode Island Red
Hatched October 14, 2012 - Latte, a mixed pullet - a.k.a. a "Fudgelet"
Hatched December 9, 2012 - Snow and Blackie, Olive Egger pullets and Penny, a Black Copper Marans
he was really hurting !
