Is the gold that the mother sold to her father to meet his needs considered a debt upon her from the inheritance, or is it her right, especially since parts of it were a dowry and a gift from the father, and other parts the mother bought with her own money?

The debt of the deceased must be paid from their estate before it is distributed among the heirs, because debt takes precedence over the heirs' right to the money, as Allah Almighty says: "from after any bequest which he made or debt." Paying off this debt and fulfilling it is a religious obligation upon the heirs before distributing the estate so that the deceased's liability may be cleared. As for the mother's claim of debt against the father, it requires sharia-compliant evidence or acknowledgment by the heirs. As long as it is a dispute, it should be presented to the Sharia court.