We had a problem with small critters pulling up our new sod and also gophers digging up holes. A product that was powedered fox pee called something like "Critter be gone" worked after 2 applications. You shake the stuff around the holes and the perimeter of the yard. Here is the link to the product. We also have a dog and needed to have something that wasn't toxic.
http://www.critter-repellent.com/index.php