This paper presents a multi-agent dialogue support framework based on a large-scale language model (LLM) to support positive family interactions. It focuses on subtle psychological dynamics that are difficult to capture with existing metrics, particularly the suppression of children's emotional expression due to "ideal parent bias." A Japanese parent-child dialogue corpus (30 scenarios) was constructed, annotated with ideal parent bias and emotional suppression. Based on this, we develop a role-playing LLM-based system that detects emotional suppression, explains implicit ideal parent bias in parental speech, and infers contextual attributes such as the child's age and background. Expert agents collaborate to generate empathic and pragmatic feedback. Experimental results demonstrate significant accuracy in detecting emotional suppression categories and generating empathic and pragmatic feedback. Follow-up simulations of feedback integration demonstrated improvements in emotional expression and mutual understanding, suggesting the potential to support positive changes in family interactions.