Merck manual lists various species of coccidia protozoans. Some can infect dogs and cats, with rodents as intermediate hosts, apparently. If the rodents are intermediate hosts, can't their scat pass it to the dogs? How, if not by poop, do rodents pass it to carnivores--in muscle? or in intestines, which of course have poop? I wonder if OP also has cats on the property, her own or ferals?
http://www.merckmanuals.com/vet/digestive_system/coccidiosis/coccidiosis_of_cats_and_dogs.html

"Hammondia has an obligatory 2-host life cycle with cats or dogs as final hosts and rodents or ruminants as intermediate hosts, respectively. Hammondia oocysts are indistinguishable from those of Toxoplasma and Besnoitia but are nonpathogenic in either host. (see also Besnoitiosis, see Sarcocystosis, and see Toxoplasmosis.)

"The most common coccidia of cats and dogs are Isospora. Some Isospora spp of cats and dogs can facultatively infect other mammals and produce in various organs an encysted form that is infective for the cat or dog. Two species infect cats: I felis and I rivolta; both can be identified easily by oocyst size and shape. Almost every cat eventually becomes infected with I felis. Four species infect dogs: I canis, I ohioensis, I burrowsi, and I neorivolta. In dogs, only I canis can be identified by the oocyst structure; the other 3 Isospora overlap in dimensions and can be differentiated only by endogenous developmental characteristics."

Note that insects are also listed as needing control to control the protozoan. Flies are nasty!