Is it permissible to invite family and friends to a wedding party where there is much amusement and dancing, and what is one's duty upon attending it?

If the matter is in your hands, move the celebration from a place of transgressions to a place free of them. It is not permissible to enter places of transgression if you cannot change them. Do not invite family and friends unless you are able to change the transgression. Do not make inviting family and friends to weddings and occasions come at the expense of religion. Avoid what is unlawful and places where it occurs, and do not invite people to places of transgression and corruption, even if it leads to their anger, for Allah and His Messenger are more deserving of being pleased.