In Texas how can estranged adult children of first marriage be sure their rights are protected upon the death of their father?

At the death of the father the adult child or children can file a claim against the estate with the probate court. Bear in mind that Texas is a community property state, that being the case the majority of marital property is automatically awarded to the current spouse if the father dies intestate. If there is a Will the "right of election" is in force and the terms of the Will dictate distribution for any separately held property. Almost any Will can be contested, however, it is generally an expensive and lengthy process to do so.