What is the ruling on joking that involves accusing parents of being lost and attempting to sell one of them to buy land, and what is the solution for dealing with the parents' anger towards the wife because of this joke?

Your wife erred in what she said, and she must apologize to your mother and seek her forgiveness and رضاها by offering a gift and admitting her mistake. Your mother should accept the apology, for whoever's apology is not accepted by his brother bears a sin like that of the toll collector. Al-Hasan (definition) ibn Ali said: "If a man were to insult me in this ear and then apologize in my other ear, I would accept his apology."