The rapid advancement of large language models (LLMs) has opened new opportunities for Emotion Recognition in Conversation (ERC). However, most existing LLM-based approaches neglect two underlying causal relationships: when utterances drive emotions, and when emotions drive utterances. These two directions closely align with the dual-system theory in psychology, which distinguishes between fast and slow thinking. To explicitly model these bidirectional causal dynamics, we propose a Dynamic Causal-Prompted Framework (DCPF), which leverages causal prompting to enhance the contextual understanding of LLMs. Inspired by the Peak-End Rule, DCPF evaluates whether the current utterance reflects fast or slow thinking and infers its causal orientation accordingly. Based on this analysis, DCPF dynamically adjusts corresponding causal prompts at each iteration to guide the LLM in modelling conversational context more accurately. Experiments on multiple benchmarks demonstrate that DCPF significantly improves ERC performance, particularly in long-context scenarios, and proves effective in both multimodal and text-only ERC tasks.