Asimov did something like that by accident - he was given a quotation by JBS Haldane, and asked to write a story about it, which he did - creating 2430AD (2430 A.D. - Wikipedia), which illustrated Haldane’s point. But the people who asked for the story wanted a story refuting Haldane - so Asimov wrote “The Greatest Asset” (The Greatest Asset - Wikipedia). Both stories were eventually published.
How about Philip Pullman’s His Dark Materials as a response to C. S. Lewis’s Chronicles of Narnia, as discussed in Skald’s thread from a few years ago: C. S. Lewis vs. Philip Pullman.
Reading that thread, I found a link to an earlier thread which might have some other ideas of the kind of thing you’re looking for here: We get that you hate that earlier writer. Stop kicking him, okay?
If short stories count, there’s been several “rebuttals” to The Cold Equations. One I recall offhand was titled The Cold Solution I think, in which the pilot used a laser welder to cut off the legs of the stowaway and herself to make up for the extra weight. Both lived.
While there are less cases than you might expect, some of the other Flashman novels are responses to previous fictional works. The strongest example is the early Royal Flash, which I take as Fraser going “here’s how Antony Hope ought to have plotted The Prisoner of Zenda, rather than throwing away a great idea on an okay implementation”.
Later books and stories echo Uncle Tom’s Cabin, The Man Who Would Be King and Doyle’s story “The Adventure of the Empty House”, where the joke partially becomes how unobservant Sherlock Holmes is.
(Hughes strikes me as unreadable and doesn’t really need to have been done so to get Flashman or its sequels.)
A Google search turns up this questionable offering…
I think that’s “The Cold Solution” by Don Sakers.