Dog-Proofing a Sloped Backyard in Kentucky

Three dogs will destroy any lawn. Options: 1) Walk dogs elsewhere. 2) Build a fenced dog run (6-10 ft wide) along a property line, mulch it, keep main lawn nice. 3) For patio mud, add a low wall uphill with a French drain. Shade + dogs = few grasses survive; limb up trees for light.