What should I do with my wife who left home and refused to return until I prove my innocence of the theft accusation at work, and what is the role of her parents in this matter, and what is the impact of that on my son?

If the wife leaves her husband's home without his permission, merely upon learning that her husband has been accused of theft, and she refuses to return, and then leaves her father's home without his permission, this constitutes nushooz (disobedience) for which the wife is sinful. This nushooz forfeits her right to financial support (nafaqa), and she must repent and return to her husband's home and live with him in kindness. Her father must order her to return. It is advised to warn her about the consequences of nushooz and family disintegration. If she persists, it is recommended to involve righteous people as mediators to guide her back to what is right.