All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the girl is living in your brother's house abiding by the rulings of Islam such as not being alone with your brother or other marriageable men, not mixing with them, not uncovering herself in front of them etc., then she may live there.
Second marriage is allowed for every Muslim if he can be just among his wives and bear their responsibilities as we have mentioned in our Fataawa 84411, 86439 and 86514.
Know that one should not contact the girl directly to know whether or not she wants to marry him, rather he should ask her guardian to marry her to him. See the details in our Fatwa 90577.
Allaah Knows best.