What is the ruling on a man being in the same room as his brother's wife in the presence of his brother, with her wearing her hijab, and is it obligatory for men to be in one room and women in another?

It is forbidden for a man to be alone with his brother's wife, due to the saying of the Messenger of Allah, peace and blessings be upon him: "Beware of entering upon women," and his saying: "No man should be alone with a woman unless there is a mahram with her," and many hadiths explaining the prohibition of a man being alone with a woman who is a stranger to him. The brother's wife is a stranger. As for one's sister, she is a mahram, and there is no harm in being alone with her. If there is no seclusion with your brother's wife and she is wearing the proper Islamic attire, there is no harm in your being in the same room, with the obligation to lower your gaze from her.