What is the ruling on eating from money in which lawful and unlawful elements are mixed, specifically if the sister's money comes from a usurious bank and is spent on the family?

Dealing with a person who possesses unlawful wealth, when that wealth is precisely the unlawful money and has not mixed with lawful money, is impermissible. However, if it has mixed with lawful money such that the dealer is not certain that he is dealing with the unlawful money itself, then dealing with him is disliked (makruh). Your sister's salary from the usurious bank is unlawful (haram). If it has not mixed with lawful money, then it is not permissible for you to benefit from any part of it. She must dispose of the remaining salary by spending it on the welfare of Muslims and seek another job free from শরিয়া violations.