So sorry to hear that she won't stop and listen. This person she is seeing might not even be telling her the truth about the marriage. I believe in a previous post that the woman told your wife that her marriage is loveless or other wise not healthy (?). If she is being dishonest with her husband by cheating, she could very well be dishonest with your wife and the husband could be sitting at home thinking everything is great.. I know that something is wrong if there is cheating involved, but the marriage could be completely different than what is being represented to you wife.
Do you know the woman and her husband? Are these people that will ask you when it all comes to light "why didn't you say anything?"
If your wife can not see how wrong this is and not care who it hurts in this relationship, what happens if the next person comes along and is cheating? Is this going to be a behavior that continues? I know that is a hypothetical question but one that needs to addressed. If this is a continuing behavior, can you stay with her?