Is the husband obligated to pay his deceased wife's debt to her mother, especially since the mother is well-off and did not give her daughter anything from her father's inheritance?

The heirs are not entitled to anything from the deceased's wealth until after their debts are settled. The debt of the deceased woman must be paid from her estate, based on the Prophet's (peace be upon him) saying: "The soul of the believer remains suspended by his debt until it is paid off." And while a husband is not obligated to pay for his wife's medical treatment, it falls under the category of good companionship and kindness. A wife's relinquishing her share of her father's inheritance to her mother is considered a valid gift if it was done during her sound health, and the heirs have no right to object. The mother's possession of a bank balance does not negate her daughter's debt to her, knowing that depositing money with interest is clear usury. In conclusion: this debt must be paid from the wife's estate before its distribution, unless the mother waives it.