Is my insistence that my father live with me in the marital home, despite my wife's discomfort and her need for privacy, an injustice to her, or is it an act of filial piety towards my father? And what is the way to satisfy my wife in this situation?

The wife has the right to a residence independent from her husband's relatives, and the privacy of her marital life must be preserved. Therefore, neither the husband's father nor anyone else should enter upon her without her permission, in observance of the Islamic legal guidelines. The husband is advised to reach an understanding with his wife and remove anything that harms her. The husband's brothers are considered non-mahram (foreign) to their brother's wife, and they must observe the Islamic legal guidelines in their interactions with her. The wife is not obligated to serve her husband's family.