Is it obligatory to donate the usurious gains that were intended for charity after the car purchased with money mixed with usurious gains and lawful money was destroyed, and its wreckage was sold?

It is not permissible to deposit money in interest-based banks except out of necessity for safekeeping, and it is not permissible to take interest on it. Rather, it should be placed in a current account. Whoever has received such interest is not permitted to benefit from it; rather, they must dispose of it by giving it to the poor and needy or spending it on charitable causes.

Your mother must repent to Allah from usury. If she knew the impermissibility of the interest before spending it on the car's price, she must dispose of it if she has money, because it is not permissible to own this interest. If she does not have money and repents to Allah, we hope that will suffice her.