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Alienation of affection is a suit against the paramour, not the spouse. North Carolina is one of very, very few states that still allow these types of lawsuits, so you would sue there, not in Texas. North Carolina has jurisdiction over a non-resident who causes a tortious injury in the state, so you will be able to sue her, even if she doesn't live there.
The conduct has to have occurred before you separated, or during a time that you were attempting reconciliation
. Basically, you want to show that this person came in and destroyed an otherwise happy marriage through malicious conduct.
You may also have a claim for criminal conversation, which is what North Carolina calls adultery. You need only show that, while you were married, someone else had intercourse with your husband.
Because these complaints are very fact-specific, the best thing to do is go to the law library and look at books that give you ideas of what you need to allege. This site has more information on these two torts:http://www.rosen.com/divorce/divorcearticles/alienation-of-affection-and-criminal-conversation/