What is the ruling of Islamic law regarding the husband's oath that his wife will not go down to his mother's house, as a result of a problem where the mother accused her daughter-in-law of theft, coupled with the mother's need for help and the wife's non-involvement in the problem?

The mother's ill suspicion was a mistake for which she must repent. However, it does not justify what the daughter said or what the son did. Rather, they must bear with her and treat her kindly, for the mother's right is immense. As for the husband's oath, he must offer expiation for it. If he insists on preventing his wife from going to his mother's house, then she must obey him.