What breed do you have? Some dogs just like to dig. When I built my fence for my aussies, I had to put ground timbers in the ground and nail the fence to them. It work wonders, although I still have one (not sure who) who loves to dig a hole next to the house and pool. I just leave the hole and they have never dug any further down.
I agree with the one designated digging area. Another soultion to help detour unwanted digging spots, and usually works for me. Is to sprinkle a good amount of ground pepper on the area. Most dogs do not like the smell, and will usually stay away from it. But, it may not work for every dog. It is pretty enexpensive, so you don't have anything to lose.
Animals, what animals? My children just have alot of hair!