Is it permissible for the sister to demand two thousand dollars in return for the one thousand she previously sent, knowing that the original was a cash loan, not gold whose value has multiplied?

The determining factor is what the borrower borrowed and received from the lender. If what was received was gold, then an equivalent amount should be returned. If it was cash, then an equivalent amount should be returned. There is no consideration for the difference in the price of gold or the change in currency value between the day of the loan and the day of repayment. What is obligatory is the one thousand dollars you borrowed, and if you add to it without a condition in the loan contract, there is no objection, as this falls under the category of rewarding a good deed. This is also in accordance with the saying of the Messenger of Allah, peace and blessings be upon him: "Indeed, the best of people are those who are best in settling debts."