Is the questioner considered responsible and accountable for the presence of the satellite dish in her mother's home, given that she is the eldest of her siblings?

The introduction of "dish" [satellite TV] into Muslim homes is an evil and a tribulation that must be fought. The religious responsibility falls on every individual in the family. The father is the primary responsible party, but this does not exempt the eldest son, especially in the father's absence, from the responsibility of educating, disciplining, and being in charge of the household. And every shepherd is responsible for his flock.