What is the ruling of Islamic law regarding a wife reclaiming her gold that she sold to help her husband purchase a car, and is this considered a debt upon him? How valid is the wife's comparison of her debt to that of his mother, and what is the appropriate solution for returning the value of the gold?

Spending on the wife is an obligation upon the husband. It is not permissible for the husband to take his wife's money unless she gives it willingly. It is recommended for the wife to assist her husband financially if she is able. If the wife gives money to her husband as a gift, she is not allowed to reclaim it, except in the case where a parent gives to their child. If the money is a loan, the wife has the right to reclaim it. The husband's permission for his wife to take her salaries cannot be considered compensation for his debt, because the salaries are her right.