Medical Vision-Language Models (MedVLMs) excel at perception tasks but struggle with complex clinical reasoning required in real-world scenarios. While reinforcement learning (RL) has been explored to enhance reasoning capabilities, existing approaches face critical mismatches: the scarcity of deep reasoning data, cold-start limits multi-specialty alignment, and standard RL algorithms fail to model clinical reasoning diversity. We propose MMedExpert-R1, a novel reasoning MedVLM that addresses these challenges through domain-specific adaptation and clinical guideline reinforcement. We construct MMedExpert, a high-quality dataset of 10K samples across four specialties with step-by-step reasoning traces. Our Domain-Specific Adaptation (DSA) creates specialty-specific LoRA modules to provide diverse initialization, while Guideline-Based Advantages (GBA) explicitly models different clinical reasoning perspectives to align with real-world diagnostic strategies. Conflict-Aware Capability Integration then merges these specialized experts into a unified agent, ensuring robust multi-specialty alignment. Comprehensive experiments demonstrate state-of-the-art performance, with our 7B model achieving 27.50 on MedXpert-MM and 83.03 on OmniMedVQA, establishing a robust foundation for reliable multimodal medical reasoning systems.