What should I do about music being played at family gatherings, and should I avoid these gatherings? What is the ruling on attending a wedding where there are drums and tambourines? And how should I deal with my brothers who are negligent in performing prayers at the mosque?

If you encounter a reprehensible act, such as musical instruments, you must condemn it gently. If you are heeded, then praise be to Allah. Otherwise, you must leave the gathering unless doing so would cause harm. As for weddings, if they involve only the duff (frame drum), they are permissible. But if they include other musical instruments, it is not permissible to attend them. Regarding waking family members for prayer, you should alert them to the importance of prayer and the danger of abandoning it, then wake them gently and kindly. If they do not respond, then you are absolved of responsibility.