Ask Mr. Smarty Plants

You apparently have two distinct problems to address.

1. Dog wallowing in damp spot and ruining plants.

2. Multiple utility systems that need protection from roots.

Much as we hate to admit it, plants are not the solution to every problem, not even native plants, which is all Mr. Smarty Plants will recommend. We are sure you don't want to get rid of the dog, or you would have already done so. There are no plants that can resist being dug up and wallowed in on a daily basis. If you could transplant something like a cactus or other succulent (of which there are 18 native to Kansas), they would not like that damp soil as they are all desert plants. And it would have to be large enough at the time of transplant to really discourage the dog, and therefore really tough to transplant. You could try putting in some large shrubs, again, large plants are not easy to transplant, and that would immediately complicate your utility line problem.

Now assuming the dog can find somewhere else in not quite as delicate a situation for the dog's cool down, we would suggest covering the area around the pipes with river rock. Not gravel, because the dog could dig that out and spread it around in a heart beat. The rock would be attractive, allow ventilation of the soil beneath it, and at least minimize weeds. Here is a previous Mr. Smarty Plants answer on using river rock where growing anything is a problem.