Is it permissible to take from money that I swore not to take, in order to pay off a debt, and is expiation (kaffarat yameen) required if I do so?

If you swore not to take money from your relative, this is a binding oath, and it is not permissible to retract it except with a connected exception. If you take the money, an expiation for breaking an oath becomes obligatory upon you due to the occurrence of the breach. If the benefit necessitates it, then do so, in compliance with the saying of the Prophet, peace and blessings be upon him: "Whoever swears an oath and then sees that something else is better than it, let him do that which is better and expiate for his oath."