Is it obligatory to boycott relatives who know about and condone a woman who commits adultery and lives off the money of this adulterer, and are their money and homes considered unlawful, despite the desire not to sever ties of kinship?

Consider a few situations that would rule out your cousin living with the man without marriage: her family is upright and would not condone their daughter engaging in immorality, and she herself is committed to the duties of religion and wears a hijab, so she would not accept an illicit relationship.

Therefore, it is advisable to pause and assume the best, that she may be married to him in a valid marriage with the permission of her guardian and in the presence of witnesses, as the lack of its announcement does not affect its validity.

Your aunt and her daughters are your relatives, so it is obligatory to maintain ties with them. If you become aware of any Sharia violations, then advise with wisdom and good counsel.