from past posting experiences, I know folks don’t always read the OP carefully so let me just bold the main points.
I live in high desert - hot in summer, cold in winter, dry all the time. I have 3 old dogs.
landlady pays the water bill and doesn’t want to use much for the yard.
the backyard in the house I rent is dirt - and now that it’s spring it’s weeds. there are two trees for shade although I don’t know if they are going to make it.
the front yard (which I don’t care too much about) is going to be what my landlady calls “desertscape” - gravel and maybe some cactus. as low maintenance as it gets.
the backyard she is open to what I want, long as it doesn’t take much water. all I want is for the dogs to have some where to hang out and low maintenance. easy to scoop poop.
nothing is perfect - I would just keep the dirt and weed-wack now the weeds - but mud when there is moisture, yuck.
we had tons of pine needles and were thinking of using that for a mulch. I would like to limit the use of toxic weed killer and use at least some nontoxic options like hand weeding, vinegar concoctions, etc.
consider a structure for dog comfort.
a short pergola to create shade. with a louvered top (at the correct angles and orientation) you could provide ventilated shade during the day.
no idea of what to do for a shitting area.
I have small dog pens (3 total) that I can move around and shade won’t be a problem at least this year, while the two trees are still alive. if they die we will have to make more shade somehow.
How about just putting down mulch?
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Having read the OP carefully, this seems to be more advice and opinion than factual.
Moving thread from General Questions to In My Humble Opinion.
Dogs love to sleep under cars,why not create a reasonable stand in?
I have three large dogs and live in the high desert, so maybe I can help.
I have a large back yard, stockade fenced, with two shade trees, one on each side of the yard. The dogs like to run back and forth along the back fence because people and other dogs walk by and I’m afraid they really like to bark.
Since they ignore the sides facing both neighbors, I installed raised flower beds there with some removable wire fencing to ‘remind’ the dogs not to jump in them. Along the back of the fence where they run, I laid down a gravel path as I couldn’t get anything to grow there with all of their usage of that area.
Most dogs, if you observe them for a while, will develop usage patterns in your yard. After figuring out where those were, I installed gravel pathways there, too. In between the pathways, I can easily grow grass for them to eliminate on or lay down on to cool off.
When I leave this house, if non-dog lover moves in, all they will have to do is remove the plastic sheeting under the gravel paths and re-seed.
We have watering restrictions, so I use a lawn product that’s specifically designed to hold water in the grass’s roots. It’s been working well for me.
Keep in mind that I don’t need to use my backyard for any recreational purposes. I have a lanai/deck that the humans use, so I was able to dedicate the grassy areas to the canines.
Would your landlady accept reimbursement for water usage over the monthly average?
Google xeriscape plants for your geographical area. I can tell you what would work here, but I do not live in high desert.
My dogs are getting up there in years too, and while I don’t live in the desert, I’ve been researching options for our new back yard (which is currently construction dirt topped with snow).
I’ve never had very good luck with grass with them, so I’m eliminating it. We’re going with a mix of concrete, paving stones and wooden deck, with the dog specific area designated to be concrete. There will be a shaded area and an unshaded area as they love to bask in the sun.
Any foliage will be in tubs or raised beds, we’re still negotiating that and will make a decision on placement after the fences are in - I have a real problem visualizing undefined spaces.
We’ve also in the past used smooth river rock for a the dogs elimination area and might keep a small area for that just for the drainage.
I just spoke with a local plant expert and he recommended decomposed granite instead of gravel for paths and such which sounds good from what I’ve read.
we are considering mulch especially since we already have a lot of pine needles
that is an excellent idea but I am already paying more in rent than I can really afford so I’m going to try and get her to pay for whatever water I use…if we do end up with some plants. I’ll make sure she understand the water needs will be higher until the plants are established and maybe we’ll just have a small area that needs watering some after that, depending. but if I win the lottery it will different!
stillownedby setters - we both want no grass at all since I don’t want to mow and she doesn’t want to water. my dogs are only able to go out on leashes so far because of all the cat poop out there -
after they eat it hours go by and then the vomit is really foul. 
but once it is covered up I hope to have paths/open areas for exercise, potty, etc.
I think we will end up with mostly no plants - maybe a small xeriscaped area. I love High Country Gardens for ideas - from their blog I found out about a crevice garden - if I owned the house I’d have one of those!
Moonlitherial - I like your ideas; whenever I’ve seen river rock used it’s very attractive and I’m thinking maybe ANY plants that I buy (rather than the landlady) are going in containers. because who knows. you might want to look into the decomposed granite options for potty area, kinder on the feet maybe? I mean if it’s fine enough - haven’t actually seen it yet but see link further up
