rutlandite,
I wonder if your Moms problem is less about the right plant in the right place and more about the fact that every type of plant needs a good watering schedule it's first year while the roots adapt. Perhaps a soaker hose along the strip would help. kt

Agreed with kt, Rutlandite... regular watering as plants are becoming established is essential, especially in a high-sun area like that. I'd also add that a good application of mulch would help retain moisture (already done?), and some basic soil amendment (some compost or other organic matter, and gypsum to help break up the clay) wouldn't hurt, either.

Reading between the lines, it sounds like your Mom is looking for something fairly low-maintenance, but it's important to remember that there's no such thing as a NO-maintenance garden! Having said that, a little initial work to create a receptive space for plants (ANY plants) will pay dividends in terms of what your Mom can plant and sustain with minimal effort in the future.

The list of potential plants is long - sedum seems a good option, but in part it depends on the look that you want to create. BTW - crocus, while a delight in Spring, spend most of the summer invisible: they bloom, spend a short time growing leaves and nourishing the bulbs for the following year, then the foliage dies back as the weather warms up, and they go dormant. Nice, definitely, but not going to work as a ground cover!

Kate's right. If crocus and sedum won't live there, I don't think anything will without some help getting established.

Some basic soil preparation - turning over the soil and adding a load of organic material before planting would be very helpful, applying an organic mulch around the plants would probably also help ensure their survival. The soil improvement only gets done once, so it's a long-term investment that keeps paying back.

You might want to try creeping thyme, some varieties are extremely hardy and almost evergreen and it grows in dry locations. A heather and heath assortment might be nice too.

But! That first year or two, everything needs water.

Thank you very much for the replies. My Mom & Dad both have
the best yard in their nieghborhood. Plant galore & a very lush green lawn. Both always tend to the plants it is just that part of the yard. I forgot to add too they tried phlox
& when they first moved in I gave them rose bushes. Even they didn't take. My Mom said they tried putting top soil down once. That did not work. They also tried with a rotertiler (sp?). She wants to try putting a weed gaurd down. That is the only thing growing & they are for ever pulling weeds. Organtic soil? What is that? She probably knows what that is, But I don't. We did come up with an idea though. Will this work? Putting a weed gaurd down &
I have 2 empty heavily wooded lots next to my house. She wants to take some soil & compost from the empty lots & place them over the weed gaurd. Will that work?

I would say to put in rocks and crushed stone. Create pockets of good planting mix and plant a succulent garden. They are beautiful, love heat and need little water.