Does the wife bear a sin or guilt for her involvement in the funds of a tobacco shop registered in her name, despite her attempts to persuade her husband to abandon it? And is there an expiation required of her for that? And does sin fall upon the husband? And what is the obligatory expiation upon him?

As for the money spent by the husband, if its source was mixed between lawful (halal) and unlawful (haram), then the expenditure is permissible, though disliked, and nothing is binding upon you. However, if it was purely from unlawful sources, and you were in need at that time, then there is no sin upon you.

As for the husband’s inheritance, what he earned from unlawful money must be given in charity to the poor and needy, or for the benefit of Muslims, and caution must be exercised in estimating this. If there is doubt about the amount of unlawful money, it should be disbursed based on diligent estimation.

As for the shop being registered in your name, as long as that was not by your choice or consent, then there is no sin upon you, Allah willing.