What is the ruling on accepting gifts from an heir of a drug dealer, knowing that the money and possessions were inherited from drug trafficking, and that the heir himself does not deal in them?

Unlawful wealth is not inherited. Rather, the heirs must dispose of it by spending it on charitable causes and general Muslim welfare. If it is known that there is unlawful wealth in the inheritance, and its amount is uncertain, then the estimated amount of unlawful wealth should be given out through ijtihad (independent reasoning). What your mother and family are doing is correct, for whoever guards against doubtful matters protects his religion and his honor.