All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
It isn`t permissible for a wife to allow any of her family or blood relatives to reside at her house except with the consent of her husband and vice versa because the marital home is the right of the wife and, at the same time, it is the property of the husband. Therefore, it isn`t permissible for any of the spouses to allow anyone to reside at marital home without the consent of the other spouse. This is in accordance with article (76) of the Jordanian Personal Status Law, which states: "It isn`t permissible for the wife to bring her children from another husband or her blood relatives to live at her marital home without the consent of her husband particularly if that home is his."
In conclusion, if the husband permitted his wife`s sister to stay with them, then this is permissible. However, the Sharia teachings, in this regard, must be observed, such as making sure that there is no risk of fitnah (sedition), lowering gaze, modesty, not wearing makeup, adhering to Islamic dress code and that the presence of wife`s sister doesn't prevent the husband from having sexual intercourse with his wife. And Allah the Almighty Knows Best.