There seems to be an awful lot of both in the US and it strains credulity.
Wait a minute, it "strains credulity" to reference common events that happen to people all the time? You'd prefer the woman gets struck in the head from a toilet set from the space station?
Yes, there are credibility issues with inconsistent ideas: a wife cheats because she's so tired of all the great sex, but I think your problem (in your question) is with the lack of believability. If someone doesn't act grief struck, then it's hard to believe his wife died of cancer or was killed by a drunk driver.
Once again, I only ask, because maybe it's the author's intent not to draw attention to the wife at all. To make her part of the story as obscure as possible so that he can focus on whatever the story is about.
In that case, you'd simply say 'he and his wife gradually drifted apart', explaining his apparent lack of concern with her disappearance. Not all explanations are consistently logical. Remember the KISS philosophy: Keep It Simple Stupid. Don't add complexity to something you want to slip under the radar. Doing so raises questions you don't want to answer.
In this case, 'showing' would include demonstrating how he feels by how he reacts. But giving details about how the wife died is purely 'telling', you're telling the readers what happened to the wife rather than fully exploring the topic.