It isn't hard to see the centrality of family to Libation Bearers. In the very first scene, we have two children paying homage to the spirit of their dead father; then they realize that they are brother and sister, which gives us a family reunion scene. The play's climax is an all-out battle of words between a mother and son, which ends with the mother being killed – talk about family drama. Probably the best way of thinking about the theme of family in Libation Bearers is that it sets the stage, or provides the context, puts up the venue, or whatever other metaphor you want to use, for the main themes of revenge and justice to play themselves out. Specifically, it's the context of family that makes it impossible for those themes to play themselves out in a straightforward way. As far families go, the royal house of Argos is about as dysfunctional it gets. This, in turn, shows how dysfunctional traditional ideas of revenge are.
Libation Bearers shows us that, even though Orestes thinks family ties are based solely on social obligation (which binds him to avenge his father against his mother), he finds out that they are actually based on nature (when he is overcome with grief after killing his mother).
Clytemnestra's different attitudes towards her children before and after killing Agamemnon show that she has become a different person since the crime.