That area that's very narrow and gets rain runoff... I would be more inclined to loosely set some pavers or stepping stones or something along those lines. Ground covers would require constantly being edged to keep them out of the already-narrow walkway.
Plant suggestions that come to mind are Oyster Plant in the sunnier spots, Wandering Jew (varietated or Purple Queen) in all the smaller areas, Wire Vine either in pots or growing over rocks. I like the way purples look with pink and magenta.
It's hard to tell from the photos you shared whether you have room for anything larger or taller?

Thanks for your suggestions, shear_stupidity. DH said the same as you about that narrow bed, and for the same reasons. I was trying to ignore him, but you make it difficult. :-)

I like your purple suggestions, and I've had good luck with wandering jew, so that would be an easy addition. What are your thoughts on sea grasses? Are they messy? I would like some height, as it would hide the pipes and pool pump.

Here's another picture. I'm mortified by the state of our beds! Thanks for your help.

African iris (Dietes iridioides) is well behaved, not messy and will hide those pipes. They'd eventually get too wide for that walkway, but might be a good companion for other taller plants near the pool. You might have to clip the football-shaped seed pods if you don't want volunteers, but otherwise, they're absolutely care-free. They do fine in sun or shade, wet or dry, hot or cold. Nothing seems to bother them. As a bonus, you can come dig as many as you want out of my yard for free. One clump can be divided into many plants, and I also have dozens (if not hundreds) of seedlings that can be transplanted. As an extra bonus, they're super easy to transplant.

There's a yellow species, too (Dietes bicolor), but that one is a real slow grower. It took two years for divided transplants to start blooming in my yard. Although they grow to about the same size, the bicolor seems more dainty than the iridioides.

I agree with Tradition about African Irises for height. A lot of grasses are sparse and don't hide so much as they camouflage. (I have some from him and they really are great!)

And I can't believe I forgot to say Coleus!!!! All of them, from the giants to the trailing ones would work well and go well with your pool area... plus it's free color without the mess! (Just pinch off seed pods of they're dangling over the pool edge)

I love those irises, Tradition, thanks! That's exactly what I needed to get me going. What else do you suggest with them? Would alyssum work in this area? I looked up companion plants, and found lavender, salvia, sedum and fountain grass. I've never been able to get lavender of any kind to grow, so I'll skip that.

Shear, we looked at pavers for that narrow walkway, today. DH thanks you!

You know what I see going in that narrow space? I would put down several layers of weed barrier and cover with pea gravel. Then I would buy all sorts of little cement or heavy plastic figures - maybe a rabbit family, a turtle family, some toadstools/mushrooms, some birds - you can see what I'm talking about.

Here is a google.com search for 'landscaping with statues' - see if anything here interests you.

Here is a link that might be useful: Landscaping with statues and figurines

If that area is particularly shady, then Alyssum would be leggy and might not bloom well for you. Plus, it's not exactly a "clean" plant. It self-sows all over the place. But if you have a sunny spot, it could work.

Tell your DH he's quite welcome!

Any plant that flowers will be dropping them in the pool, you'd be better off with colorful leaves on a plant.

That's why I was thinking Coleus... and Perilla Magilla, and Persian Shield...
Hardly any flowers and easy to pinch off as they come.

Again, thanks so much for the suggestions. I'm so drawn to flowers, but I'm admittedly not the one cleaning the pool filter. Kay, my kids would just love those little statues. :-) After spending the day digging that mess up, I'm looking forward to seeing what the nursery has. Such colorful plants, Shear. I love the shades of green and purple!