What should I do about my family's leniency in playing music at home, which has affected my devotion in prayer and the non-acceptance of my supplications?

Faith increases and decreases. Your family's leniency regarding watching television and listening to music might be due to their weak faith and lack of fear of Allah, for Satan gradually leads a person from permissible acts to forbidden ones. You should advise your family and remind them of Allah. Avoid gatherings of evil, associate with righteous company, and supplicate frequently with humility for an increase in faith.