Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
There is no objection for this woman to go out during the day but she should return home at night. Imam Al-Nawawi said: "It is lawful for the woman who is in her Iddah following the death of her husband to go out to satisfy her needs (such as buying food, or selling things or weaving… and the like. She is also allowed to go out at night to visit her neighbors, talk to them, etc., but she should not spend the night with them. Rather, she should return to her home and sleep there."
Sheikh al- Islam, Ibn Taymiyah said: "If she (the widow in her Iddah) goes outside to satisfy some needs and she does not spend the night outside her house; then there is no harm in doing so."
All the above is enough evidence that the widow (while in her Iddah) can go outside at the night or during the day provided she does not spend the night outside her house.
In addition, there is no objection to her visiting her ill brother. As for attending his funeral, this is dislikable, not because of being in her Iddah, but because this is dislikable for women in general. Um Atiya said: "We were told not to follow the funerals. But it was not made forbidden for us to do so."
Allah knows best.