Is it permissible to falsely swear to one's wife to avoid separation due to previous illicit relationships, and what should one do with a woman who tries to stir up trouble between him and his wife?

The husband should improve his relationship with his wife and make her feel her importance so that she forgets the girl's stance. He should completely ignore the girl without informing his wife or anyone else about what happened, because Allah is "Modest, Concealer, who loves modesty and concealment." Knowing about it might lead to severing family ties or divorce. She should be reminded indirectly about concealing sins and warned against causing strife among Muslims. The husband's lying to his wife and denying what the girl said is permissible; it is one of the types of permissible lies for reconciling disputes and preserving good marital relations, as the Prophet (peace be upon him) said: "He is not a liar who reconciles between people, conveying good or saying good." This includes a man's conversation with his wife. As for swearing an oath regarding it, it would have been better not to swear. If he had to, it should have been by insinuation. Since a false oath was taken, he must repent and seek forgiveness. Al-Shafi'i held that expiation is obligatory in such a case.