Is it permissible to sit in a place where music is played—such as a home or at relatives' houses—without the intention of listening or enjoying it, especially during mealtimes or when visiting relatives?

You must advise your family and your sister gently and kindly, enjoining upon them what is right and forbidding them what is wrong to the best of your ability, and clarifying the impermissibility of listening to music. If they do not respond, then you are absolved of responsibility. You should sit in your room and distance yourself from them when they play music. If there is a necessity to sit with them, such as for eating, there is no harm in that, provided you do not listen intently, or actively hear, or watch.