Have you thought of putting up trellises and covering them with an evergreen vine? Either crossvine or Confederate jasmine can take a lot of sun and heat, and are pretty impervious to diseases and pests. Container plants such as blue agave or another drought/heat tolerant succulent could be put between the trellises, perhaps under the two windows.
Just don't attach the trellises to the brick! Give at least two feet of air circulation in back of the trellises.
Also, apricot trees are notoriously difficult. Good luck with your new garden!

I have a similar location, sun-wise. What kind of soil do you have? These are the plants that have done well for me:

Big Plants:
Waxleaf Ligustrum
Crepe Myrtle
Columnar Juniper (I wish I could tell you what variety it is that we have, because it's great, but it was here when we moved in. Be cautious, some are better than others.)

Medium Plants:
Salvia - Blue Henry Dualberg (I'm sure I spelled that wrong)
Rose of Sharon
Blue Mistflower
Hardy Plumbago
Hardy Hibiscus
Nandina

Small Plants:
Rainlilies (with a little protection, like underneath a larger plant)
Lantana
Mexican Heather
Phlox or Thrift
Mexican Petunia
Gayfeather
Blanket Flower or Firewheel
Artemesia
Daylilies
Sweet Alyssum
Mums
Cuphea
Butter and Eggs Wildflowers
Bluebonnets

Vines:
Passion Flower
AMERICAN Wisteria (not the Chinese!!!!)
Carolina Jessamine

Anacanthus is you want hummers by the gajillions in there too! PJ

I agree with PJ that a Flame Acanthus would do well and look great. I also have cassia "trees" and some are like shrubs that would do well and give you blooms in the fall until frost. I know that there may be some who disagree with me, but I have also found that Turk's cap does well and blooms more in part sun.

Marlin Gardener, Mommy Fox, PJTX Girl, and Carrie 751,
Thank you so much for the wonderful and abundant plant suggestions for my problem area. The trellis idea is inspired and I love the tall junipers (have two smaller ones on the front (North side)of the house...but not in hot sun). Right now the soil in that location is "builder's cement" (aka rock hard red clay) but I'm hoping to import several yards of good garden soil and perhaps build a raised bed (if I can afford one that length). The Anacanthus and Cassia bushes would be perfect, too. All I could think of before y'all came to the rescue was: cactus, cactus, and more cactus...but even cactus would not put up with heavy shade until mid-afternoon...if I'm not mistaken.