Cross-subject electroencephalography (EEG) emotion recognition remains a major challenge in brain-computer interfaces (BCIs) due to substantial inter-subject variability. Multi-Source Domain Adaptation (MSDA) offers a potential solution, but existing MSDA frameworks typically assume equal source quality, leading to negative transfer from low-reliability domains and prohibitive computational overhead due to multi-branch model designs. To address these limitations, we propose the Hard-Easy Dual Network (HEDN), a lightweight reliability-aware MSDA framework. HEDN introduces a novel Source Reliability Assessment (SRA) mechanism that dynamically evaluates the structural integrity of each source domain during training. Based on this assessment, sources are routed to two specialized branches: an Easy Network that exploits high-quality sources to construct fine-grained, structure-aware prototypes for reliable pseudo-label generation, and a Hard Network that utilizes adversarial training to refine and align low-quality sources. Furthermore, a cross-network consistency loss aligns predictions between branches to preserve semantic coherence. Extensive experiments conducted on SEED, SEED-IV, and DEAP datasets demonstrate that HEDN achieves state-of-the-art performance across both cross-subject and cross-dataset evaluation protocols while reducing adaptation complexity.