Human Activity Recognition (HAR) using wearable sensors has great potential in healthcare, yet centralizing sensitive data raises privacy concerns. Federated Learning (FL) offers a privacy-preserving solution but often struggles with data heterogeneity, fairness, and personalization. To address these challenges, we propose FedMMD, a novel FL framework that integrates a Multi-gate Mixture-of-Experts (MMoE) architecture with a client-aware aggregation strategy. The MMoE enhances generalization and prevents expert collapse through contrastive learning, while the aggregation scheme adapts to client-specific data characteristics, improving fairness and personalization. FedMMD is evaluated against FedAvg, FedProx, and FedNova on three widely used HAR datasets. Results show consistent improvements in accuracy, F1-score, and recall, demonstrating robustness under heterogeneous conditions. Beyond performance, FedMMD ensures equitable treatment of clients with diverse data distributions; a key requirement for real-world healthcare deployment. Overall, FedMMD advances privacy-preserving healthcare by enabling scalable, reliable, and personalized HAR without compromising sensitive user data.