so.....what do you need help with? As long as the animals are present, you'll have bare spots where they scratch or run/dig.
No plant can withstand that.
Eat the chickens, and walk the dog. Like Walter Said, not much you can do if they run around on the ground. They will tear it up.
I am concerned about runoff and erosion as this is on a slope. In my perfect world, the chicks will stay in their run and the corgi will adopt another hobby. No eating the chickens. They are my egg makers. I need a fast growing ground cover that grows in sun and shade and that I can start now. Walter, I am counting on you to come up with a good solution! Surely you have an idea or two. Thanks to the chicks and the corgi, the ground is nice and soft.
You might try some ground cover, some sort of ivy, lariope, artemesia is also a good ground cover. Ground covers work well on a slope because you won't need to mow. Check with your local extension agency to see what kind grows best in your area.
Walter Reeves is right! I labored to put in a 25'x3' stone pathway complete with accent stones, timbers, flower beds, expensive varigated border grass only to adopt a black lab the next year. She is so wonderful I do not care how the back yard looks! It is a worthwhile swap off!
Are you trying to plant something tall/dense enough that the chickens and corgi will then not go on the slope? Do you have a way to keep them off until the plants get established?
Yes, I can keep them off until it is established. If it grows tall then it will have to be mowed--well, it will be mowed anyway. In parts of my yard the mint goes wild and that is nice until it dies late in the summer, so I don't have a problem with something out of the ordinary. Let's just say that this is not your regular suburban back yard. The front yard is politely in compliance with the neighborhood covenants. The back yard is um, a little more, ah, native.
Why not plant something like Carolina jessamine and let it scramble like a ground cover? Or take a look at creeping raspberry. Or plant the slope with ornamental grasses.
or maybe creeping liriope (Liriope spicata)
We have liriope in our dog's fenced area and she loves it. in fact when we let her out among the grass out front (and the lilies), the hunkers down like she is hiding. It became a "plaything" for her. But then dogs are known for being silly and entertaining!
I went out and bought liriope, planted it carefully and the chicks got out and
"moved" the poor little plants several times. So I soaked a bag of pinto beans and planted them everywhere there is a bald patch. Everywhere--all over the yard. My dog Cowboy watched me plant them and came behind me, delicately pawing them up and munching raw beans. But he didn't get them all! The chicks have demonstrated that they don't care for beans and they are leaving these little plants alone. At least I will have ground cover and add nitrogen to this soil. We will see what the pinto bean plants look like.