Is it permissible to use a sum of money to meet the needs of one's mother and brother instead of paying off an interest-based debt (riba) secured by gold jewelry, in order to discontinue dealing with usury after becoming aware of its prohibition?

Spending on oneself and on those whose maintenance is obligatory, such as parents, takes precedence over paying off debt. This includes providing suitable housing. If the mother's house is not fit for habitation except by renovation, then its renovation takes precedence over paying off debt. However, if it is fit for habitation and the renovation is for perfection or adornment, then paying off debt takes precedence. You are not obligated to pay off your brother's debt; rather, your only obligation is to pay off your own debt.