What is the ruling on the husband's behavior towards his wife and father, and is it permissible for him to remain married given the existence of this suspicious relationship, taking into consideration that he does not know the extent of the wife's coercion?

It is impermissible to accuse a Muslim of committing forbidden acts without clear evidence, especially if the accusation is of adultery, which is only proven by the perpetrator's confession or the testimony of four upright witnesses. This prohibition is even stricter when it comes to accusing one's father. If a son is certain or strongly suspects that his father has committed an abominable act toward his wife, he must immediately separate her [from his father] and prevent his father from being alone with her. The son should not prolong his absence from his family, and he should advise his father gently and kindly if the matter is proven, without using it as a reason to harm him.