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My gut feel in this situation is to have an attorney go with you or turn down the request. The request seems odd, and the manner the request was made is also abnormal.
You need to be careful. North Carolina is one of a few states that allow lawsuits against parties for "Alienation of Affection". This works 2 ways a jilted spouse can sue your husband for damages, and/or you can sue the other party's spouse for damages. It really depends on who pursued who, and if your husband has a history of chasing women this will not work out well.
In the first case if you support the fact that your husband ruins marriages the other side may be able to file suit and get damages from your husband which of course will decrease the marital estate.
Conversely if you tell the other side your marriage was already broken then you will not be able to request damages from the other party if you were so inclined. The other lawyer may be trying to find out what you knew and the current status of your marriage to avoid possible damages later.
If as a witness someone tells you that if you have a lawyer they cannot talk to you, that means you are going to be a party to a lawsuit. What you say can cost you money in or other aggravation in the long run. It has been my experience that lawyers set up their own meetings. The fact a PI is asking you to met with a lawyer is odd to say the least.
My suggestion is that if the attorney wants to speak with you ask your husbands attorney to attend with you, or bring you own attorney along with you. If your statement is really needed they can formally depose you once a lawsuit is filed. Once filed you will be able to ascertain the nature of the legal proceeding, and who the parties are. Given you now know abut the affair you should speak to your husband about what is going on, and whether he is being sued.
The other admittedly remote possibility is that your husband is staging this meeting to try to get information from you in preparation for a divorce. It is possible that although the PI represented to you that the attorney was working for someone else, the attorney is really working for your husband. I know this sounds underhanded, but stranger things have happened. The fact they are asking about you having counsel makes this very suspicious, and it should make you very cautious.
If you do attend the Thursday meeting make sure you understand who the attorney represents from the attorney himself, and the purpose for your being requested for a meeting. You should also ask why your statements are important for the case.
If you do attend you should not discuss your current relationship with your husband, You should not discuss his other extra-marital affairs. If asked indicate that is better answered by your husband. Keep in mind that if you talk to the attorney you may compromise your spousal privilege at a trial or hearing.