Is it permissible for the wife to receive the husband's brother in the husband's absence and allow him into the house, and what should she do if she stays with a neighbor to avoid being in seclusion with him?

There is no objection to the wife receiving her husband's brother at home, provided certain conditions are met: the presence of someone who negates seclusion (khalwa), not seeing what is impermissible, and that the husband does not dislike him. If these conditions are not met, then he is not permitted to enter the house. It is permissible for the woman to spend the night outside her home to avoid seclusion, provided her husband gives permission.