You are correct - lawns do not fair well in very shady areas even without dog traffic :-)

The choice you need to make is if you are willing to give up all pretense at a back garden because of the two large dogs or if you can carve out some dog-free patches to plant with shade lovers. I'll let you decide, but my choice would be the second. It is possible but may take some creativity, effort and attention to remedial dog training:-) Some combination of hardscape - pavers, graveled pathways, barked areas - and raised planting areas may work. I suggest raised because elevated plantings tend to get trampled less easily than do ground level ones. Be sure to allow enough space for the dogs to run and do their thing. And there are always containers.....you could plant them up seasonally for color or larger, more permanent ones to provide ongoing green and living interest.

For northern California there are scores of plants you could use as long as you can keep them dog-free long enought to outgrow trampling or juat plain out of reach of the dogs. Perennials or other groundcovers just will not hold up sufficiently on their own unless you can keep the dogs off.

Hi & welcome to GardenWeb.

I only have 1 dog in my yard but he's huge - a great dane. He has paths that he constantly uses through the yard - one straight from his dog house to the back porch, one around the perimeter of the fence, and one going from side to side, semi-circling around the back of the house. Nothing but a fence would deter him from his normal routes, it's just what he does. Once you see where your dogs are going to make paths, you'll know where to not bother trying to grow grass or anything else. Then you can decide how to proceed - pavers, wood chips or pea gravel in timber boundaries, whatever you want to look at that you can afford.

My back porch is a painted wooden deck and although the yard is mostly grass, the dog has worn the paths I mentioned down to the dirt. Just the amount of moisture in the dew every morning is enough to cause dirt to stick to his paws so the deck is always really dirty with paw prints. So that's a consideration in regard to building a deck, any naked dirt from dog paths is going to end up on the deck.