The thorns suggest Blackbrush Acacia, it's present in South Texas.
It resprouts vigorously when it is disturbed but can be managed using herbicides
This depends much on your view of using herbicides, even if you do use them they would probably resprout from the running roots. The only effective way I have found to remove invasive roots is to just keep digging them out, wait a while to see what starts to grow again as you will surely miss some, then dig out what you have missed but make sure not to break any off while digging if that's possible.
http://uvalde.tamu.edu/herbari...
Cat-claw Acacia has thorns the shape of a cat's claw..
http://www.californiadesert.go...
I can't advise on what type of grass will grow best for your situation, someone else might be able to.