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.