Answer: There are several ways to approach this. In my experience, some dogs just love to dig into or nap on freshly disturbed soil. Sometimes, if allotted their own special spot for this they can be trained to limit their activities to the designated area. Alternatively, some dogs can be taught to respect a short little fence serving as a visual reminder of "do not cross".
There are special repellent sprays available under several brand names. Look for one labelled specifically for the animal you wish to repel and be sure to apply and reapply per the label directions.
Cats seem attracted to the newly disturbed soil and freshly laid mulch in the spring, to some extent it seems to be a seasonal problem. Once the plants grow larger and cover the ground they are no longer so attracted to it. You can try the sprays as above, or try to make the area less appealing. Some methods would include changing to a different mulch material and wetting the mulch layer when you apply it to compact it somewhat and render it less diggable, sprinkling thorny clippings (such as rose prunings) on the ground around the plants, covering the soil with tin foil (cats hate to step on it) and even poking little sticks into the ground to make walking difficult. Strewing bits of citrus peel may also work. There are also sonic repellers for cats and motion activated water hoses to serve as cat scarers.
There are a few plants that might repel cats such as lavender and rue (only the rue would be winter hardy in your area), but in my experience they walk right around them. The annual plant Coleus canina has been marketed as a repellent for both cats and dogs; the recommended spacing is one plant every thirty inches around the perimeter of your garden and of course you would need to replant every spring.
I hope this gives you some ideas.
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