I can only tell you what I did, and what worked for me. I told my wife that I had no intention of "sharing" her, or in living in a marriage with a third person. I insisted that she end it, and come back and work on our marriage and our issues, including the ones she had with me. I didn't put a time frame on it, but I did say that my patience wasn't indefinite.
I also told her that I wasn't going to be her "best friend" (we'd always been best friends) while she was having an affair, because "best friends" don't do that to each other. I was civil, and we carried on our business as parents caring for their children, but we didn't go on "dates" nor did I make any efforts to meet any of her emotional needs that weren't being filled by her boyfriend.
And I absolutely did everything I could to not enable her affair -- cut off her cellphone, stopped paying for Victoria's Secret, refused to lie to cover for her, even to our children and her parents.
Not everyone can pull this off, and only you know what is best for you. But I think it's reasonable to assume that if someone gets some of their needs met by their boyfriend, and the rest of their needs met by their husband, and both allow that to continue, then the wayward wife really doesn't need to make any hard choices or decisions.
There is nothing "rude" or "insensitive" about insisting that your wife respect her wedding vows. If anything, she will RESPECT you for it, as mine did, and told me later after she ended her affair.
