Am I sinful if my family listens to music and is negligent in prayer, knowing that I have advised them and explained to them its importance and the punishment for abandoning it?

You do not bear the sins of your family, just as they do not bear any of your burden, as Allah Almighty says: "And no bearer of burdens will bear the burden of another." You must advise them, enjoin upon them what is right, and forbid them what is wrong, especially regarding the danger of being negligent in prayer. It is not permissible for you to sit with them while they are committing a forbidden act, such as listening to music. You must leave them if they do not heed your advice, unless you are compelled to stay with them, in which case there is no sin upon you.