What is the ruling on the adult nephew (sister's son) remaining in the same house with the questioner's wife, who does not observe hijab in front of him, and his niece (brother's daughter), who also does not observe hijab in front of him, knowing that there is no other place for him, and the questioner is the one who raised him upon the fear of Allah?

Your nephew is a stranger to your wife and your niece, and they must observe hijab in front of him. This hijab, according to the preponderant opinion, includes the face and hands. If there is difficulty and hardship in this, then there is no harm in uncovering the face and hands when there is no fear of fitna, as long as the young man is pious. The young man must lower his gaze and avoid khalwa (private seclusion) with your wife and your niece. This fatwa is supported by the principle "Hardship begets ease" and Allah's saying: "So fear Allah as much as you are able."