What should I do regarding my father-in-law's pressure for me to divorce his daughter, whom I have not yet consummated the marriage with, despite the issue between us having ended and my refusal to divorce, and his rejection of mediation and prevention of his daughter from communicating with me?

What we advise is to make an effort to resolve the issue with the wife's father by apologizing and involving righteous people as mediators. If he responds positively, then praise be to Allah. If the problem persists and the wife is righteous, then her father's demand should not be succumbed to. He must fear Allah, for the sin of seeking to separate spouses without a legitimate Sharia-based reason is grave. It is not permissible for the wife to obey her father in boycotting you or demanding a divorce due to the absence of a legitimate Sharia-based reason. It would have been more appropriate for the father to be a helper to his daughter in maintaining her marital life. As for the wife's father's pretext that you slandered his daughter, this claim is incorrect if nothing was uttered by you except the phrase you mentioned, because you merely recounted what you heard and did not confirm it; rather, you sought to explain to her the methodology followed in dealing with such rumors.