How should the money be returned in this case: should the same amount be returned in cash, or the value of the grams that were sold?

The obligation in a loan is to return its equivalent. It is not permissible to agree to return money as gold, or to return gold as money, whether the gold is raw or manufactured. This is because such an arrangement is considered a sale of gold for money with a deferred قبض (seizure/possession) of the price, which is impermissible; rather, it is usury (riba). Current currencies take the place of gold and silver and share their rulings. Therefore, whoever gives money to take gold must do so hand-to-hand. Consequently, the brother should return to his mother the equivalent amount of money he took, and stipulating the return of gold is not permissible.