It isn't defined in a statute. Look to case law. Where do you primarily live? Sleep at night? Get your mail? Address on your driver's license? Address on your federal tax return? Tell ICE to contact you? "Domicile" has nothing to do with citizenship or country of origin. Why don't you get a lawyer and let a professional deal with this? When you're ill, do you diagnose and treat your own illness? Do you do your own auto repairs?
I am not intending this to be legal advice, because I don't know the particulars of your situation. Call me if you would like to discuss this or other isues.
I agree this is not addressed in the Texas Family Code, and instead is addressed by case law. To be a domiciliary of Texas you must have a fixed place of abode in Texas. The case law defines that constitutes a fixed place of abode, and there are a number of relevant factors. No one test applies to all situations.