I just read in Daily News yesterday about putting in fake lawn. It's becoming big business and much approved from years past. I'm not sure how dogs would react to it and if they like to dig.
There are tons of natives you can use without using prickly cacti that dogs wouldn't like. Here is a couple sites for information.

http://www.laspilitas.com/
http://www.theodorepayne.org/
http://nativeson.com/

I might work from the edges of the garden inwards, eliminating the grass, improving the soil, and putting in shrubs and trees, while deciding what groundcover can resist the dogs and what design you prefer. Tearing up the whole yard all at once will be disruptive for them and challenging for you. Especially if you have something like bermuda grass, which 5 years after going native with no dogs, I am still fighting.

Do you want a dog playground, with tunnels (culvert pipe) and climbing structures (old tires) as well as nontoxic shrubs for shade and the obligatory fenceline path (if your dogs like to patrol the boundaries)? Or do you want a pleasant outdoor room for yourself that is relatively low-maintenance and indestructible? How big are the dogs, and how old are they? Do they like to run outside, or dig, or fetch? Are they water dogs? Are they mostly indoor or outdoor dogs? Will they be left alone outdoors for hours at a time (free to get into trouble if there's nothing to engage their attention), or will they be in the yard only when you're home?

If you have a doggie daycare in your area, you can ask for a tour and take note of what kinds of play structures they have.

If your dogs like to chew sticks and you're looking for nontoxic shrubs, the number-one shrub to avoid is oleander. Also stay away from thorns, prickly leaves (can hurt paw pads), and grasses with large awns that can get caught in fur or inhaled. If they put everything in their mouth, avoid toxic berries.

Wood chips are great for paths -- better than gravel for dogpaths, and less likely to get caught between toes, unless your dogs are older and have trouble walking, in which case hardscape is easier.

You'll also want a designated doggie bathroom area. Are your dogs trained to go in a specific area, or on a specific substrate? For some years we had ivy-trained dogs, which was great, especially for walks around the neighborhood. (The new dog likes to go on lawns, alas.) If I had large dogs in my yard, or dogs who eat or roll in poop (I've known labs and a beagle...), I'd get one of the composting bins made especially for dog waste -- compact, and requires much less handling of poop than plastic bags.

Other dogcentric features include dog-height fence holes so the dogs can keep tabs on neighborhood activity; lots of trees to attract squirrels; a patch of groundcover for rolling on their backs; dog-height paths and tunnels through shrubbery...

If you're building a patio area (shaded seating) for yourself, then think about where the dogs will lie down when you're outside -- most dogs like to do some exploring, then come sit next to their pack leader. Make the patio area large enough to accommodate everyone.

With three dogs, I gave up on having a lawn a long time ago. Cedar Bark mulch is now where there was once lawn. I put more on every year.

I am struggling with the same problem...trying to train my dogs to pee in one spot. Any suggestions? And does anyone know of a groundcover that is dog pee resistant? I do know that there is fake lawn made specifically for dogs. Although it's out of my price range!

Here is a link that might be useful: artificial dog lawn

One theory for getting your dogs to eliminate in the same spot is to keep them penned, or crated up, until they MUST go and then lead them to the spot you want them to go in. Praise them. Repeat several times. It is easier if you get them to go at the same times each day to create a routine.