Is it permissible to go with a cousin to help her with the preparations for her wedding party, which will include music and songs, knowing that attempts to convince her to suffice with only the duff (tambourine-like instrument) have been unsuccessful?

It is not permissible to help in preparing and furnishing places where unlawful acts are committed, nor in the preparations for celebrations that include forbidden acts. As for helping with permissible preparations for the bride, such as buying clothes or household necessities, this is considered assisting a Muslim, for which one is rewarded. This is considered helping someone who intends to commit a sin in matters not related to their sin, and there is no evidence to prohibit this.