Dogs dig. It's their nature. Use bricks and add dirt to fill their holes. After scraping claws on bricks, dogs will decide that this isn't fun after all. They also enjoy scraping off huge sections of lawn, leaving bare dirt. Lay chicken wire, burying edges deep so they can't pull the wire out. Over this, lay St. Augustine sod. Wire effectively discourages digging in gardens, too. But it makes future planting difficult. Dogs may repeatedly dig in the same spot to get at underground decaying matter. One way around that is to cover those spots with brick squares topped by decorative planters.
Many herbs and pungent flowers perfume the air when dogs plow through. While that won't discourage the canines from doing their thing, it's a silver lining to cling to when beds get trampled. Although small-thorned or prickly bushes such as barberry and hollies will discourage some dogs, resist the urge to plant varieties with long, lethal thorns or points, such as yucca. These might injure a dog's eyes. Sometimes a mulch that's uncomfortable or uneasy to walk on will work. A thick carpet of pinecones, for example, discourages even steamrollers.
Be willing to compromise. Turn a dog's favorite route into a decorative pathway and landscape around it. To keep dogs on track, consider lining the path with raised beds or ornamental fencing. Another option is to divide the yard, giving the dog a private area that is at least partially shaded.
Line pathways with soft materials (pine needles or leaves) that dogs will like. A pretty but uncomfortable paving will send dogs on new routes. In a fenced-off section, add a sandpile for digging, safe toys, and a flat-roof doghouse so they can get on top and survey their domain. Dogs like that. By the same token, if you have a stockade fence, leave a small window for them to see through.
Remember that dogs, like people, are all different. It may take a lot of experimenting to see what works for both you and your pet. The important thing is to keep your sense of humor. Remember, dogs think their behavior is perfectly normal and you're the one who's not cooperating.