Get the lowdown before you go.
Before your girlfriend tosses you into a minefield, ask her to illustrate a lay of the land. Does her grandpa have a tendency to tell long stories while sporadically spitting? Is her dad sensitive to discussions about current events? These are helpful things to know before going into the line of fire.
Conversely, it's also helpful to know a little about each of her family members. You may have gleaned some of this from conversations with her, but ask her to fill in the blanks. Where does her little sister go to school again? What teams do her family support? All of these details provide natural segues into conversation. If she says her dad is big on golf, you know chatting him up about the PGA tour will guarantee a lively discussion.