Perceiving overall classroom emotion is crucial for effective teaching, yet existing methods lack robust, evidence-based reasoning and interpretability for complex multimodal data. We introduce EduInsightLLM, a novel hierarchical framework that decouples perception from reasoning to address this challenge. Specialized Video and Audio Large Language Models first extract structured semantic evidence from classroom recordings. A central Reasoning LLM then integrates this evidence, performs conflict resolution, and makes an educationally-grounded emotion classification. Critically, the model generates a natural language explanation that is explicitly grounded in the multimodal evidence it cites. To enable this, we construct CER-6, a new dataset of multimodal classroom clips with fine-grained emotion labels. Experiments show that EduInsightLLM significantly outperforms strong baselines in classification accuracy, while its explanations are rated highly by human evaluators for their faithfulness and coherence, demonstrating its potential as a trustworthy educational analysis tool.