Who is the brother-in-law (al-hamu) according to Islamic law, and is it permissible for the wife to live in a house with her husband's married brother when there is no privacy except for the bedroom?

"Al-hamu" refers to the husband's brother or a male relative of the husband, while "al-khatn" refers to the wife's brother or a male relative of the wife. The husband's brother is a stranger (non-mahram) to the wife; in fact, he is more deserving of being prevented [from being alone with her] because he can access what others cannot. The Prophet, peace and blessings be upon him, said: "Beware of entering upon women." It is not permissible for a non-mahram to reside in the same house with a woman unless each of them has exclusive use of all facilities and they do not share anything.