Is it permissible to stay overnight in a house that was purchased with ill-gotten money, knowing that the reason for staying overnight is family problems and a rejection of certain behaviors? And is it permissible to boycott a sister and expel her friends who encourage her in behaviors that are not in accordance with Islamic law?

There is no harm in staying overnight at your brother's house even if his money is from illicit sources, and there is no harm in your father working in customs if his work is not forbidden. You must be gentle with your sister and invite her to Allah with wisdom and good admonition, and avoid violence with her. Advise her to abandon friends who incite her to disobedience. You can gently prevent her friends from entering the house if she persists in associating with them.