You need to immediately contact an attorney in TX to determine what the children's rights are in this situaiton. I suggest you call an attorney in the county in which the house is situated as opposed to trying to get an answer on an Internet forum such as Avvo. While Avvo is great for general information, specific facts would be helpful to properly advise you. Many attorneys will answer your preliminary questions via a free consultation with no cost to you.
Attorney James is correct. You should be consulting with local Texas counsel (in the county where the property is located) for an in-depth factual analysis of the situation. You can contact the local bar association or use the Avvo Find a Lawyer Tool.
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Talk to a Texas lawyer. Some states grant spouses special rights regardless of what the will says and the wife may have special rights under community property law. I doubt you can do anything effective by simply not giving your birthdates.