Is it permissible for the husband of your other cousin to stay in your house with his wife for a week or more, in your and your uncle's absence, while your uncle's wife, your wife, and her divorced sister are in the house?

It is permissible for your female cousin's husband to sit in the house if he is trustworthy and does not see your wife and her sister. The husband of a woman's sister is not a mahram (definition) to her, and it is not permissible for him to be in seclusion with her or for her to expose any part of her body to him. The Prophet, peace and blessings be upon him, emphasized the matter of the hamw (a husband's non-mahram relative), saying: "The hamw is death." This is due to the great temptation that may result from people's laxity in this regard, as it becomes easy for him to approach and be in seclusion with the woman.