High-quality, social interactions between parents and their children are crucial for young children's development. In order to develop affective, intelligent interactions between parents and children, it is important to understand how the parent's nonverbal behavior influences the child's affective state. In this paper, we explore the role of a parent's nonverbal cues on a child's engagement during an educational, dialogic reading interaction. We specifically focus on using synchrony in the parent and child's body pose features and affective states to better inform a child's engagement during the task. To understand the moments when children lose engagement in a task, we qualitatively assessed video clips and found that those moments are associated with either the parent or the child exhibiting actions unrelated to reading the stories, such as yawning or the parent checking their cellphone. Finally, we provide an overview of design implications for parent-child facilitator AI systems as well as future research directions in this area.