Is a wife's intense feeling of hatred towards her husband's mother, while outwardly showing her good treatment and respect, considered hypocrisy? And what should she do about this feeling?

Continue to be patient with your mother-in-law, overlook her faults, and forgive her, for these are good deeds through which you hasten to Allah's forgiveness and His Paradise. Persist in this, and do not surrender to Satan by retaliating in kind. Forgiveness and patience are among the great virtues to which Allah has enjoined His servants and promised reward for. Know that your feeling of being a hypocrite is incorrect; rather, it is from the wiles of Satan. Showing courtesy to people is a characteristic of believers and not hypocrisy; it is about being humble and gentle in speech, and it differs from the forbidden flattery. You can advise her and point out her mistakes in a gentle and kind manner.