What is the ruling on attending my sister's wedding, which includes loud music (DJ), when I disapprove of it, especially given that there is no mixing of genders and my family needs my help on that day?

Songs accompanied by music are forbidden. As for those devoid of musical instruments, such as songs limited to the drum (daff), there is no harm in them, especially at weddings. If a wedding banquet includes forbidden songs, it is not permissible to attend it, due to the Almighty's saying: "And He has already revealed to you in the Book that when you hear the verses of Allah disbelieved in and ridiculed, do not sit with them until they enter into another conversation. Indeed, you would then be like them." So, everyone who sits in a gathering of disobedience and does not condemn them will share in the sin. If the invited person knows there is a forbidden act and cannot remove it, then it is forbidden for him to attend. However, if he can remove the forbidden act, it is obligatory for him to attend and condemn it. The general rule is that it is not permissible to invite anyone to a banquet that includes forbidden songs. If there is a place at the banquet where the songs cannot be heard, then it is permissible to attend and sit there. The fact that the banquet is for one's sister's wedding does not permit attending forbidden songs.