Your wife has no greater rights than you. Your daughter has been in Texas for at least six months so Texas is now her "home state". Texas will have jurisdiction in a custody matter. However, I don;t know anything about your wife's past contacts with Texas, so it's impossible to discuss jurisdiction regarding divorce. I suggest that you contact a family lawyer as soon as possible.
You need to file a petition for divorce immediately. Texas courts have in rem jurisdiction over the divorce. Texas courts also have jurisdiction to determine the custody status of the child here in Texas. You need to get an order saying that this child stays in Texas. She may choose to object to lack of personal jurisdiction over her, if she has not lived in Texas or subjected herself to the jurisdiction of courts in Texas, but that doesn't change the fact that you need to file for divorce and custody immediately.
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You have established residency in Texas. You need to consult an attorney
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