Ask Mr. Smarty Plants

Your problem may be two-fold.   First and foremost is the issue of shade.   Very few grasses will grow in the shade and, moreover, even fewer turf grasses will grow there.  

As a substitute for grasses in your shaded areas you might consider grass-like sedges or other groundcovers.  You can read about the advantages of having a sedge lawn in the article, Sedge Lawns for Every Landscape, by John Greenlee.  Here are three sedges that will do well in Harris County:

 Carex texensis (Texas sedge)

Carex cherokeensis (Cherokee sedge)

Carex flaccosperma (blue wood sedge)

You can see a list of "Native Groundcovers" for the Houston area from the Houston chapter of Native Plant Society of Texas (NPSOT) in its Native Plant Guide.  Here are some possibilities from that list:

Calyptocarpus vialis (Straggler daisy) will grow in sun, part shade and full shade and tolerates moderate foot traffic.

Phyla nodiflora (Texas frogfruit) grows in sun and part shade and spreads by trailing runners.

Mitchella repens (Partridgeberry) is a trailing evergreen that does well in the shade and part shade, but needs adequate water and doesn't do well in areas of high traffic.

Polystichum acrostichoides (Christmas fern) is an evergreen low-growing fern that loves the shade and would do well in areas where these is not a lot of traffic.

There are several plants that do well in the shade and attract hummingbirds and butterflies.  Lonicera sempervirens (Coral honeysuckle) will grow in part shade and can serve as a groundcover.  Fire spike (Odontonema strictum) is a native of Central America and thus, with our mission—"to increase the sustainable use and conservation of native wildflowers, plants and landscapes"—is not a plant we would recommend.  A beautiful native substitute is Malvaviscus arboreus var. drummondii (Turk's cap or turkscap).  Both Aquilegia canadensis (Eastern red columbine) and Aquilegia chrysantha var. hinckleyana (Hinckley's golden columbine) do well in the shade and attract hummers and butterflies.  Here are a some others that do well in the shade:  Salvia coccinea (Scarlet sage), Lobelia cardinalis (Cardinal flower) and Salvia lyrata (Lyreleaf sage).  There is a list of "Native Plants That Provide a Food Source for Hummingbirds" on the Native Plant Guide (shown above) from the Houston Chapter of NPSOT where you can find more plants.

Secondly, your Carya illinoinensis (Pecan) may be defending its space—that could contribute to why you are having trouble getting any other plants to grow underneath it. With this defense mechanism (called allelopathy) pecans and all members of the Family Juglandaceae (Walnut Family)—walnuts, hickories, butternuts, and pecans—make and release a chemical called juglone that adversely affects many other (but not all) plants growing near them. The Juglans nigra (Black walnut) appears to produce the most, or at least, strongest dose of juglone.  It can be found in all parts of the black walnut tree—in the roots, the leaf litter and fruit on the ground.  The juglone in pecans doesn't seem to be as strong as that of black walnut and juglone doesn't seem to affect grasses or sedges, but it still might be a factor.  One thing you might do to lessen any possible effect is to remove leaf litter from the ground.  I have found several lists for plants that are resistant to juglone from the Northeast but haven't had any luck with lists for Texas or the Southwest.  Here is information for reducing the effects of juglone and a list of plants from Auburn University that are susceptible to and plants that are resistant to juglone.

Here are photos from our Image Gallery of some of the plants listed above:

Carex texensis

Calyptocarpus vialis

Polystichum acrostichoides

Lonicera sempervirens

Malvaviscus arboreus var. drummondii

Aquilegia canadensis

Salvia coccinea

Salvia lyrata