Meals are a central (and messy) part of family life. Previous design framings for mealtime technologies have focused on supporting dietary needs or social and celebratory interactions at the dinner table; however, family meals involve the coordination of many activities and complicated family dynamics. In this paper, we report on findings from interviews and design sessions with 18 families from the Midwestern United States (including both partners/parents and children) to uncover important family differences and tensions that arise around domestic meal experiences. Drawing on feminist theory, we unpack the work of feeding a family as a form of care, drawing attention to the social and emotional complexity of family meals. Critically situating our data within current design narratives, we propose the sensitizing concepts of generative and systemic discontents as a productive way towards troubling the design space of family-food interaction to contend with the struggles that are a part of everyday family meal experiences.