What should I do if my fiancée's family insists on holding a mixed-gender wedding party, and I do not wish for that, fearing it would violate Islamic law, while my fiancée holds fast to the party as her first request?

Announcing a marriage with a celebration is permissible and recommended by Sharia, provided it is free from forbidden acts such as singing accompanied by musical instruments, immodest dancing, the mixing of women with non-mahram men, and the exposure of 'awrah. If the celebration is free from these matters, then the wishes of the fiancée and her family should be met. Legitimate amusement and singing with the beating of the duff are permissible therein, as narrated by Al-Nasa'i from Ibn Mas'ud, may Allah be pleased with him. However, if it involves uncontrolled mixing or forbidden singing, then it is not permissible to agree to it.