Pets will trample out plantings. And if you fence them out to protect the new groundcover, then maybe you don't need it. For most effective coverage the planting will need some height, as might be provided by salal. Another favorite is kinnikinnick. Both want well-aerated soil, are slow to establish. Mulching at planting particularly helpful with these.

Several of the dwarf mat growing Cotoneaster species/cultivars might be good choices, and some of the lowest growing Junipers such as Juniperus conferta might work well for you. I don't know if Hypericum calycinum is considered drought tolerant in your area, but it works well with just occasional water in such a situation here in northern California.

Weeds come through creeping mats quite readily, at least during the early years. The hypericum is tall and dense enough to be good at weed suppression but very prone to rust. In the open up here its leaves are also subject to winter damage, so that mowing it down each year at end of winter may be required to maintain appearance desired by many.

Even then you still have the problem of the rust.

To keep dogs off, you want something fairly substantial. Salal doesn't discourage my dogs, I can tell you that. They love to go crashing through it. Creeping mahonia does to some extent, and that's a local native also. Junipers and cotoneasters are good suggestions, just not the really prostrate ones. Something about knee-high is more likely to keep dogs off. Maybe creeping rosemary, or shrubby potentillas.

You could also plant a low-growing hedge as a barrier, and then plant whatever you want for the ground cover.

I used to work at Lewis & Clark in the early 80s while it was still beautiful. There was tons of ivy and st johns wort and my male Samoyed especially loved running through those. It was over knee-high and he still loved the sound and feel and crashing around in it.

All the neighborhood cats troop thru my yard and the only thing that seems indestructible is the marsh buttercup. But that's for swampy areas. I doubt anything keeps dogs off. Maybe dwarf mugo pines?

Warty barberry is pretty common in parking strips and other landscaping here, with its vicious spines it might be better at diverting pets than shrubs that do not have them.

But again, as with deer if you fence the animals out then you are no longer subject to what they might do.