Is it permissible for a widow undergoing her waiting period (iddah), who suffers from asthma and lives in a small house with her deceased husband's brother and his family, to leave her room and sit with and meet her husband's brother in the presence of family and children, given that her circumstances do not allow her a separate home?

A woman whose husband has died sitting with men and meeting them has nothing to do with the waiting period (iddah). Whatever was permissible before the iddah is permissible during it and after it, and whatever was not permissible before the iddah is not permissible during it or after it. She must remain in her home and not leave it except out of necessity or dire need. It is permissible for her to move around within the house, and she is not obliged to remain in one room, especially if she is harmed by that.