In this work, we discuss a theoretically motivated family-centered design approach for child-robot interactions, adapted by Family Systems Theory (FST) and Family Ecological Model (FEM). Long-term engagement and acceptance of robots in the home is influenced by factors that surround the child and the family, such as child-sibling-parent relationships and family routines, rituals, and values. A family-centered approach to interaction design is essential when developing in-home technology for children, especially for social agents like robots with which they can form connections and relationships. We review related literature in family theories and connect it with child-robot interaction and child-computer interaction research. We present two case studies that exemplify how family theories, FST and FEM, can inform the integration of robots into homes, particularly research into child-robot and family-robot interaction. Finally, we pose five overarching recommendations for a family-centered design approach in child-robot interactions.