What should a wife do if she doubts the source of her husband's money, especially with children present, and should she continue to live with him or distance herself from him?

If the doubt is without justification, it is a bad assumption about a Muslim and should not be paid attention to. However, if there is a justification, such as the husband selling prohibited items, then if it is known that all his money is unlawful, it is forbidden to accept any food or clothing he brings her. She is allowed to refuse until he provides a lawful allowance. If his money is mixed with lawful and unlawful sources, it is not forbidden to take from it, but it is disliked.