Is the husband obliged to separate from his family if they commit sins such as cutting off kinship ties, consuming ill-gotten gains, and gambling, knowing that the family is unaware of the source of the unlawful money, and that the husband repents then returns to committing sins?

You must repent to Allah with sincere repentance from sins and evil deeds. Unlawfully acquired money must be returned to its owner if known. If not, it should be given as charity on his behalf to the poor and needy, or used for the benefit of Muslims. Money gained from gambling must be given as charity to the poor and needy, or used for the benefit of Muslims. There is no need to separate from the family, but rather to rid oneself of any unlawfully acquired money in one's possession.