What is the ruling of the Sharia regarding a mother's insistence that her son divorce his righteous wife, her claim that not divorcing is an act of disobedience to her, while the spouses wish to remain together?

A husband should treat his wife well and not obey his mother in divorcing her without cause. Obedience to the mother in this regard is not obligatory and may even be impermissible. Imam Ahmad explicitly stated that he does not approve of a man divorcing his wife at his mother's command, unlike the command of a just father.

The wife should help her husband in honoring his mother, strive to treat her well, and overlook her mistakes. This is part of noble character and perfect kindness towards her husband. The husband, on the other hand, should be wise and combine honoring his mother with treating his wife kindly.