What is the Shar'i ruling on a husband who suspects his wife of infidelity with one of her relatives based on ambiguous actions and words, with no material evidence of the infidelity, and does conditional divorce take effect if infidelity is proven after swearing by the Qur'an?

You must think well of your wife and not accuse her based on mere suspicions, for Allah Almighty says: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." And the Prophet forbade a man from suspecting his wife of treachery. You erred by making divorce contingent on this matter, but the divorce does not take effect as long as the wife denies it. Fear Allah and live with your wife honorably, seek refuge with Allah from Satan, and fulfill your duty of guardianship over her by keeping her away from temptations, private seclusion, and suspicious mixing, then think well of her.