Is it considered usury for a mother to take 200 Saudi riyals from her son and use it to pay off a debt she owes, while another 200 Saudi riyals belonging to the son remain in her bank account?

As long as you have given your mother permission to dispose of the money, there is no harm in it. The transaction is treated as a loan, for it is stated in Kashshaf al-Qina: "If he borrowed it, meaning dirhams and dinars, to spend them, or generally... it is a loan." Some scholars have permitted the depositary to dispose of the deposited money if he has wealth and is able to fulfill the obligation, because dinars and dirhams are not designated themselves, and it is permissible to return their like. Therefore, contemporary banknotes are not desired for their essence, but rather for their equal value, so there is no difference between them and their equivalents.