What is the ruling of Islam regarding someone who publicly accuses his mother of stealing his wife's gold, then it becomes clear that the mother is innocent and that the wife and her brother were involved in orchestrating that accusation?

What the son did to his mother by accusing her of theft and exposing her is a grave act of disobedience (ʿuqūq) and a clear sin, for honoring one's parents is an obligation, and harming them is forbidden by Allah Almighty's command: "And your Lord has decreed that you worship none but Him. And to parents, show good treatment" (Quran 17:23), and by the Prophet's (peace be upon him) saying: "Stay with her, for Paradise is under her feet." Disobeying parents has been counted among the greatest major sins.

The son must repent to Allah with sincere repentance, apologize to his mother, obtain her forgiveness, and treat her with kindness, never harming her again. He must also beware of his wife's negative influence that could spoil his relationship with his family, and he should not be a mere tool in her hands.

The wife must be righteous, bringing her husband and his family together through good deeds, and not sowing enmity and hatred.