What is the ruling on a man marrying a righteous woman without his mother's consent, and what should he do about the problems that arise between the mother and the daughter-in-law, and the mother's favoritism among her sons' wives?

Obeying the mother is a religious obligation, but her disapproval of a marriage does not affect the validity of the marriage contract. As for a mother differentiating between her sons' wives, if it is merely a preference for one of them in good treatment without overstepping the bounds of Allah or severing ties of kinship, then there is no sin upon her. However, if it incites hatred, then it should be abandoned. But if the differentiation is an attempt to cause animosity through unlawful means such as lying and slandering, then it is forbidden and she must be advised.