What is the ruling on holding a wedding party in mixed-gender halls with music and dancing, and is it permissible to apologize and separate if the bride's family insists on that?

Wedding parties where women mix with non-mahram (definition) men, or which include prohibited music and immoral songs, are not permissible. Your objection to holding such a party is a necessary adherence to Sharia (definition) and a commendable zeal. You are not permitted to comply with them in this wrongdoing, even if it leads to the dissolution of the engagement. If men are in one hall and women in another separate hall, and the party does not include prohibited music or immoral songs, then there is no objection to it. Singing and playing the duff (tambourine) at a wedding are permissible, provided they do not include anything prohibited.