Is the ongoing charity (sadaqah jariyah) recorded for the questioner and his father, or for the volunteer who paid the money from her private account, or is it recorded according to the intention?

Deeds are judged by intentions, and you will get what you intended. So the money is an ongoing charity (Sadaqa Jariyah) on your behalf and your father's, according to your intention. As for what your sister did by purchasing, it was based on your promise, not with the intention of charity on her own behalf. You are obligated to fulfill the promise or compensate. Your sister will be rewarded for her effort, not for the money, because she did not intend it as charity on her own behalf.