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She would not be emancipated because she gave birth, but that isn't what you need to do.
Your son has rights to possession and access. He needs to file a Petition in Suit Affecting the Parent-Child Relationship requesting that he be adjudicated as the father, appointed a Joint Managing Conservator of the children and have specific periods of possession and access. Since the children were just born, he will have step-up possession and access. It may be in short, frequent periods at first and should be a Standard Possession Order by the time the children are three -- most likely sooner since the step-up period is starting when they are a week old.
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