Is it acceptable for a wife to perform Hajj on behalf of her deceased sister without her husband’s permission, especially since the husband bore the expenses of the Hajj? Is the wife considered blameworthy for this action? If so, what must she do to clear herself, and how can she calculate the Hajj expenses to reimburse her husband?

The questioner's performance of Hajj on behalf of her sister is valid, as long as she has already performed Hajj for herself. As for the husband, he must fear Allah and repent to Him for his acts of reminding [of his favors] and causing harm. Reminding [of favors] is one of the major sins, according to the Prophet's (peace be upon him) saying: "Three people Allah will not speak to on the Day of Resurrection, nor will He look at them, nor will He purify them, and they will have a painful torment." And among them he mentioned the one who reminds [of his favors]. The questioner is not obligated to pay her husband for the expenses of Hajj.