You say you have documentation that she has been warned about the problems?
If that is the case, I would say to her that for the reasons already provided her, the company is no longer in need of her services. If she pushes for additional reasons, tell her that there have continued to be complaints from customers. DO NOT show her the complaints or tell her specifically who complained, no matter how hard she tries to force the issue. The last thing you want is her going directly to the customers about how "they got her fired".
If you have documented the problems, and especially if you have documented the previous warnings and reprimands, that will go a long, LONG way to defending any suit she may try to bring.
For the record, Texas is an at-will state which means that you can terminate her for any reason that is not specifically prohibited by law. Nothing in your post shows indicates that she will have any kind of case to bring.
If you have not documented the problems in her file, I would give her a "last-chance" warning, documented ON PAPER in her personnel file, preferably with her signature or a witness verifying that she refused to sign. (And yes, I would have a witness, preferably her manager, your manager, or the head of HR, present at the termination.) In the event that you go the last-chance route, spell out SPECIFICALLY what needs to change and give her a limited time frame (30 days is reasonable) in which you need to see significant improvement. Make sure she understands that unless you see IMMEDIATE and on-going improvement, she can be terminated even before the end of the 30 days and be darned sure she knows that her job is on the line.
However, I would only go this route if you cannot pull documents out of her file that show she's been warned about this. (Warnings are not required by law, but they can be a significant part of a defense if she tries to file a wrongful termination lawsuit.) It sounds as if she's had plenty of chances, and if you've got the documentation I see no reason to wait.