Help with a barren yard

I live in N. California zone 9 b. Our front yard, the only part of our property that is fenced. It is a bunch of weeds that we mow and pretend it grass.  Unfortunately the foxtails have taken over. I read the main way to get rid of them is to crowd them out.  My plan was to start buffalo grass in trays, then cut it into chunks and plant on the yard hoping it would fill in.  We had 3 little dogs that don't like to be outside, so I figured/hoped it would work.  Before the weather got nice enough to try this. We got an unexpected gift?  3 German shepherd puppies just showed up in our backyard. We never found the owners, so now, heaven help us they are ours.  They are outside about 75%of the time.  They dig, and chew up everything. They all got sick this week, so we decided to remove a giant oleander.  They dig around it and chew on the roots.  The vet said this is not what made them sick, one oleander leaf will kill them.  Anyway it's gone. I never liked it because it's so poisonous, but it was nice looking, and provided a lot of shade from the afternoon sun.  
Now we have a dry dusty weedy yard.  Eventually I will plant some new trees, but at this point the puppies would just destroy it.    I'm posting this wondering if anyone has any suggestions. Something that grows fairly fast, and is drought tolerant. We are having a major drought, and I have no business trying to put in a lawn, but I hate the dry dusty yard for us and the dogs, and there's the crowding out the foxtails .
I have thought about covering the ground with cardboard and wood chips. My family is totally against having wood chips by the house no matter what I say, plus I wouldn't know what kind of wood chips and I could see the puppies eating them. No really they eat everything. If you want to clean your yard get 3 German shepherd puppies they will find every old nail, spoon, shingle, plastic toy, they will find and eat everything.  
I want to give the pups as much room as I can, we will extend the fence as soon as we can. But for now I could use some temporary fencing to block off a section to grow something.  We can mow, but it would be nice not to have to, everyone is pretty busy.  It doesn't have to be a grass, I'm open to just about anything but mint. My son hates mint with a passion unfortunately, because they sell a low growing soft mint, that would be perfect, if only.  Anyway, grass, clover, flowers, herbs.  Needs to be something easy to grow ideally something that fills in (if I get something to grow, the pups will dig, going for Gophers). So it would be nice if it would fill in once they move on. Something drought tolerant .  Right now full sun. Clay soil, but is actually pretty good soil, I can usually grow just about anything .  I will add a few pictures of the yard from different angles.  Thanks

We got two new dogs exactly a year ago this weekend. Our front yard was an overgrown mess of shrubs and weeds, and the beginnings of some raised garden beds. I removed the shrubs and transplanted elsewhere, finished the garden beds, added a fence to enclose this side of the yard (only 25' x 20') and laid sod on a ~8' x 20' section.
The grass abuts the fence and garden bed on two sides, the other two sides are woodchips, 3' border next to the house, 1' along another fence. All around the garden beds are woodchips.
I am very happy with the woodchip border! I wish that was what I did all around the grass, since mowing wouldn't also involve trimming.

Maybe a woodchip border would be acceptable?
And also the fence line might be a difficult high traffic area with the dogs "on patrol"? or it might be a difficult shady area to grow a "lawn"?
Anyways, a 4' border could significantly cut down the "lawn" area required.

You could also plant some trees or shrubs to provide for shade for the dogs, and mulch with woodchips around those (again reducing the "lawn").

To share my yard with my dogs and give them enough exercise/running space,   I used some cheap wire panels to fence a second garden fence about 8-10 feet in from the perimeter fence. It also serves to make a space where wildlife can get away and move through without getting grabbed.      I also put in two island beds with similar wire fence around them.  those have shade trees and some shrubs/perennials in them.   So it leaves lots of open space for the dogs to run in figure 8s and gives me a whole lot of growing spaces too.  

So it's along the lines of woodchip border mentioned, but doubles as privacy and growing space as well.   Trees, shrubs, evergreens, fruit bearing, perennials, etc.  

I can't comment on the grass areas itself;  different climate/species.

Jen, I'm in the same exact boat with you. Sans the puppies. Plantain is the weed we've got in abundance and some nasty sort of crab grass that is hard to yank up (of course the burrowing bastards don't eat either of those). Also some other low growing pokey plant as in it does and acts like grass needles, has little purple flowers when it's alive. So imma watch this thread in case a suggestion works 😜