Does spending time in the garden decrease stress?

Yes, yes, yes.... gardening does help with stress big time, but only if one enjoys doing that type of work.

I remember back when I use to be out 8 hours on a weekend pulling weeds [great stress relief, just think of that weed as someone who has ruffled your feathers].... putting down heavy bags of mulch... trimming bushes... etc.

BUT, as we age we cannot enjoy gardening as much as we are not nimble any more. I found myself squatting down to pull weeds then I couldnt get back up... oops. So you will need to take that into consideration for your Mom if she is physically able to garden.

Or just go to Home Depot or Lowes, and pick out some flowering plants and put them on the deck, front porch railing, or where ever and let Mom be in charge of watering and pruning. Place the flowers where she can see them. There are large plastic light weight flower containers that are great for a half dozen plants.

My backyard was looking like a wild habitat so I hired a fellow to clean it out. Wow, he did a great job. Finally it was nice to look out back and see how neat and tidy it is as I had neglected it for years, just didn't have the time or energy :(

Now, regarding your Mom's headaches, this is the high pollen season and that can play havoc with ones head. And/or if your Mom wears glasses, might be time to get new lenses.

The cure for this ill
Is not to sit still
Or frowst with a book by the fire,
But to take a large hoe
And a shovel also
And dig 'til you gently perspire.

And then you will find
That the sun and the wind
And the djinn of the garden too
Have lifted the hump
The horrible hump
The hump that is black and blue.

From "How the camel got his hump," one of Rudyard Kipling's Just So Stories. Mind you, the particular 'hump' he's talking about (the whole poem goes on quite a bit) are the blues that descend from "having to little to do" - which may apply to mother but probably rather less so to the caregiver.

For some people gardening is a blessing, for others, an evil chore. Years ago I hated yard work of any kind. I have bad hayfever so even mowing the grass was avoided at all costs.
One day, after moving in with mom, I had the worst day of bad days at work. The stress of the job at that time was a killer. I was angry, on the verge of tears, and in no mood for anything. At home the lawns needed mowing badly and with rain coming next day, it had to be done now. I was swearing up a blue streak, kicking the lawnmower as I rolled it out to the front yard. Oh, I was hating life right then.....
Mowed front with enough time to also mow the back (not small yards either). That looked good enough to make other areas look bad...so out with the trimmers and clippers I went.....Awhile later, I noticed a miracle....I was no longer stressed or angry. Tension in my body was gone, my headache was gone, and I was humming without a thought of work in my head. I felt positive about things and felt excited as I watched the yard shape up. Had you told me this years before, I would have thought you stupid or crazy or both.
Flash forward 5 years....it's one of my favorite things to do. I love it. When I feel icky I go play in the yard. From easy clipping flowers to hauling giant rocks, making my own soil to chopping down trees, building trellises or redesigning the layout there's something for any mood I might be in. There is also something about working the earth with your hands that is very grounding. Watching something you've nurtured grow and thrive is peaceful. Seeing your accomplishments right in front of you is a huge boost.
Now that's just me. I think people either love it or hate it. But it doesn't have to be all or nothing. I think it's the creativity involved that matters. Take this idea and tweak it to suit your mom's interest (if she has any).
You could do a large planter scene. You pick a theme and build a village or fairy forest (or whatever you like) using miniatures or around the house items. It's a putter project as you build/change it/watch it grow. It's super creative without the chore gotta get this done feeling. Create an area for mom to work on it that works with her strength and mobility etc and there's no heavy lifting...yayy.
Any idea you have can be tweaked or altered to suit your needs. Gotta think outside the box. There's hundreds of neat ideas online too. Start small and build on things as your mom progresses on her ability. Another thing I do to destress is paint. Paint anything from walls to custom wine bottles. Again, I think it's the creativity of it.

I find there's never just one answer to a problem either. If the doctor was right and just garden to alleviate the problem we'd all be landscapers now, wouldn't we. I know your hands are full but you are her advocate. Research on line different things that could be a cause or solution. Try different things. Works? Great. Not work? Next.
Before any doctor app of mom's, I research what my concerns are, what I'm looking for, and ask opinion on what I'm thinking of trying. I put the doc to work. I don't just take their response as the golden word. If the doctor doesn't work with me, or is always shutting me down, I find one more suitable. Not to hear what I want, but one who interacts with us on all levels of health. I do believe in Mind/Body/Spirit and all three must be nurtured to have health and peace. I don't want a doctor that minds the body but ignores the rest.

Hope I helped even a tiny bit.
Good luck.

It depends on the person but yes, gardening can relieve/reduce stress.

Some people love "playing" in the dirt. And sunshine gives Vitamin D.

Just being outdoors brings a physiological response: blood pressure and heart rate decrease, and deeper breaths are taken. The doctor's advice was not a patronizing pat on the head, it was good advice. Mom and I would "tour" the yard, looking at and remarking on flowers and plants as they budded and blossomed. It might be a good idea to spend some time with your mother in the garden (or anywhere else she would enjoy being outdoors) before sinking time and money into a major landscaping that might not be necessary, and might be stressful in and of itself. Hoping your mother finds relief from those headaches.

I remember back in the 1950's and 1950's, some doctor would tell a patient who comes in feeling not up to par, for women to go out and buy a new hat.
I wonder what they told their male patients?

Dear Mary,

I think this is only one option. It never hurts to be outside enjoying the sunshine. There are so many ways to reduce stress. I think being in a garden is one of many ways. I know its expensive to renovate a backyard. Maybe even having some extra flowers or lawn ornaments might do the trick.

Fresh air, gentle exercise and the glories of nature are good for most people. And many people do find pleasure and relaxation in gardening. But you know your mother: has she ever shown any interest in these things? Do you have any public gardens or gardening clubs near you that you could perhaps take her to for a taster?

I see that your profile explains that vision problems are your mother's main concern. Is that why you took her to the doctor? How old is your mother, and what are the worrying symptoms?

It's been a long time since I've come across the kind of doctor who would pat someone patronizingly on the shoulder and tell them their symptoms are all in their head, I've got to say the idea gets my hackles up. There are lots of ways to relax and de-stress, gardens can be lovely, but so can the beach or meditation or a day at the spa, there is no one size fits all.
And given his less than helpful treatment plan I wonder how deeply the doctor bothered to look for a cause? At the very least excess anxiety can be treated, and so can pain.

Gardening or any activity outside naturally reduces stress. It is always best to try natural "cures" rather than medicating every time there is an ache or pain or problem. If the headache seems severe, she should be thoroughly checked in case it is an aneurysm or dangerously high blood pressure.