What is the ruling on watching television with family to follow series and programs that may contain inappropriate scenes or musical advertisements, and what is the ruling on watching beneficial programs that involve mixing [between genders], and how can one act when facing these recurring situations without isolating oneself from family?

You will be rewarded as are those who patiently abstain from sins. You must take control of the remote to watch committed and documentary channels for benefit and to spread good. If they insist on watching what is forbidden, then temporarily retreat to your room to read something beneficial or memorize Qur'an. Allah will compensate you with happiness and tranquility. Participating in evil makes you like them, as Ibn 'Uthaymeen mentioned. It is obligatory to boycott gatherings in which there is evil if you cannot change it. As for beneficial programs that include advertisements or music, avert your gaze or temporarily leave. Do not completely isolate yourself from your family, but be strong in faith and do not participate with them in watching forbidden things.