I love creating stories, dramas, scandals and complex romances in my game - but one issue happens time and time again, and this seems to be an interaction that's built into the base game.
Whenever one of my Sims has gained a "cheater" reputation, his or her spouse will randomly try to "accuse (the sim) of cheating", and the interaction cannot be stopped. The alleged 'cheating' might have happened before they even met - it seems to make no difference. The interaction happens at random points, and then there seems to be no way to save the marriage. They'll be angry, and betrayed, and no matter how quickly or intensely I repair their relationship ('smooth recovery', 'apologise' etc.) and get them back in love with one another, after a couple of days, the accuser will decide that their relationship cannot be saved, and they will just automatically divorce.

Is there ANY way in which I can stop this from happening automatically, and I can be fully in control of whether they divorce or stay together?

I can sometimes avoid the "accuse (the sim) of cheating" interaction by keeping its targeted Sim really busy, as the interaction only happens at the end of his or her list, and sometimes the accuser temporarily gives up. It's annoying not to be in control of it, but I can live with it.
I just want to stop the Sims from automatically divorcing (whatever the state of their relationship) a few days later because they decide that the relationship cannot be repaired.

Any help with stopping this interaction/automatic divorce would be greatly appreciated.
Sim lives are at stake here!!

Yeah, this is normal game behavior. I've heard many a story about people whose sims' broke up because they forgot to break up with the person they went to prom with on reddit. I have managed to have a sim agree to stay together after being cheated on, but that required the cheater to grovel to his fiancee pretty much constantly, and wish for love with her from a genie...

There is a mod, NRAAS Woohooer, that overhauls a lot about how romance and jealousy works, but that also introduces a lot of other features that you might not want. But unfortunately, at least from my searching, this seems to be the only mod that affects jealousy, so if you want to change it, it kinda seems to be your only option. I just wish I could do more to help, but I don't know quite enough about modding to make the changes required.