All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the reality is as mentioned - that the girl was raised as a Christian while her father is Muslim - then she is considered an apostate. This is because she is Muslim in principle, because a child follows the best religion of his parents. If she was Muslim and became an apostate later, then attending her marriage is not allowed as her marriage is not valid anyway, neither to a Muslim nor to a non-Muslim. Moreover, attending a party knowing that prohibitions will be practiced is not allowed, whether the invitation is from a Muslim or a non-Muslim. Undoubtedly, the marriage ceremonies of non-Muslims and disobedient people are never free from improper dressing of women, mixing and touching between the opposite sexes, shaking hands, kissing and even hugging, as is known. Therefore, accepting such invitations is not allowed and keeping away from them is an obligation. See Fatwa 84976.

Finally, your cousin should know the seriousness of his negligence to his children. He should also to repent to Allaah in order to make up for his mistakes. He has to make all efforts to call his children towards Islam and to stimulate their interest in it. We hope that this might expiate some of his sins in neglecting the responsibility of raising his children Islamically. 

Allaah Knows best.