Conversational multimodal emotion recognition MER requires reliable prediction when language acoustic or visual observations are missing or unreliable. Many missing-modality methods reconstruct absent inputs yet such recovery can be non-unique in dialogue context and nonverbal cues may conflict with the target utterance. To this end we propose CoRe-KD Complete-view Reference-guided Knowledge Distillation a state-anchored conflict-regularized complete-view distillation framework for robust conversational MER. A complete-view teacher provides structured references including prediction-level references fused states and modality-specific states. Complete-view State Anchoring CSA aligns incomplete-view student predictions and states with these references while Nonverbal Conflict Exposure NCE trains on target-preserving nonverbal conflict views to reduce donor-label bias. Experiments on IEMOCAP and MELD with CMU-MOSEI as a supplementary utterance-level check show consistent gains under fixed- and random-missing protocols. Comprehensive ablation studies and further analyses support the role of CSA and the complementary effect of NCE.