How do I stop pets going in my backyard and going to the bathroom?

Motion activated water sprayer...

Do you have any friends with dogs? If so, ask if they will save some fur for you after brushing. Spread some of the "scented" fur in the garden. This should deter the cats as they can smell the dog.

Not much you can do. Stay home one day wth hose in hand and spray them every time they come in yard. Talk to owners.

Any cats I've known hate lemongrass

Citrus really drives them out. You can use orange peels around, or they have a special product that you can sprinkle around that smells like oranges. You can also plant lavender, lemongrass, lemon thyme or other strongly scented citrusy plants and that can help.

Lawn ornaments that make a sound when you walk by. Many Halloween ornaments do this - noise will scare them away.