What is the ruling regarding the dowry and gold in the event of a son divorcing his wife due to "reasons of honor, placing impurities in food, and light-fingeredness," and the family relinquishing their daughter after going to court?

If a woman is divorced before consummation, she is entitled to half of the dowry. If it is after consummation, she is entitled to the full dowry. She may waive her right willingly and of her own accord if she is of sound mind, or through her guardian if he deems it to be in her interest. This waiver is permissible in Islamic law, as Allah Almighty says: "Unless they [the women] forgo it or he [the husband] in whose hand is the marriage tie forgoes it. And to forgo is nearer to righteousness. And do not forget graciousness between you. Indeed, Allah is Seeing of what you do." If the waiver is in exchange for divorce, it is a Khul' (dissolution of marriage initiated by the wife). If it is after the divorce, it is an act of forgiveness and waiver.