H2C's inspired response:

"I don’t think fertilizer will help you much if the dog doesn’t leave the picture. I’ve had a similar problem in the past. I had a neighbor who would let his dogs run every where, and they would dump all over my yard, and destroy it. To exasperate the problem he also had live chickens that would destroy my vegetable garden. I solved the problem by feeding the dogs raw chicken for a whole week then stopped. This took care of the chickens and my neighbor then took care of the dogs. My solution won’t help you but I think you’ll see a different way to look at your problem. Best of luck."

I've added to it.