Is it permissible to perform Hajj with one's wife and mother while the wife is in debt, and she has agreed to waive part of it, and the mother will bear part of the wife's Hajj expenses?

There is no objection to the questioner performing Hajj with his wife and her mother. This is considered cooperation in righteousness and piety. The amount of expense the mother will bear for her daughter's Hajj must be clearly known. As for the debt that the wife relinquished in exchange for her and her mother performing Hajj, it has been forfeited. If the husband fears his wife might deny her waiver, he may document the matter with witnesses if he wishes. This action is permissible as long as it is by agreement of the concerned parties.