What is the religious ruling on paying expiation (kaffarah) for unobserved fasts from two past Ramadans? And should it be paid to charitable organizations? And is it obligatory upon the family? And what is its amount?

If the questioner has not reached puberty, then nothing is incumbent upon her. However, if she has reached puberty, broke her fast, and has make-up days from the previous Ramadan (definition), and then delayed making them up until the next Ramadan without a valid excuse, then she must make up the fasts and feed a poor person for each day she delayed making up, unless she was unaware of the impermissibility of delaying the make-up, in which case feeding is not obligatory for her. The amount of feeding is a mudd of food (approximately 750 grams of rice) for each poor person, which she pays herself or delegates a charitable organization to do so. If she does not possess the money, her family is not obligated to pay the expiation; rather, she pays it when she is able.