Emotion regulation (ER) is an essential skill that significantly impacts children’s social and emotional development. While prior research has shown that parents play a critical role in shaping their children’s ER abilities, the challenges and complexity in parental-involved ER interactions call for technology that delivers context-aware and personalized social support. Although social robotics and Large Language Models (LLMs) both show promise for ER facilitation, few systems integrate language-based reasoning with embodied actions to address mental health needs effectively. To expand the potential applications, we developed an LLM-powered robotic system to facilitate ER in parent-child dyads. We adopt a supervised autonomy approach to integrate natural language dialogues with physical robotic behaviors for multimodal interactions. We detail the technical implementation and interaction design of the system, along with preliminary user tests involving six parent–child dyads. The findings highlight the positive user engagement and trust in interactions with the LLM-powered social robot. Accordingly, we discuss design insights and implications in developing LLM-powered multimodal and autonomous social robot systems for family-centered mental health applications.