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You ask, "Otherwise, what exactly is the harm? This is none of his wife's business, nor his childrens'."
Really? This may actually be bigger than you think since it likely violates everything the wife understands about marriage, family and her relationship with her husband. He needs to get tested for a sexually transmitted disease, confess to his wife and ask her to be tested as well. At least those actions would prove he has some respect for her as a human being.