Federated Learning (FL) presents a groundbreaking approach for collaborative health research, allowing model training on decentralized data while safeguarding patient privacy. FL offers formal security guarantees when combined with Differential Privacy (DP). The integration of these technologies, however, introduces a significant trade-off between privacy and clinical utility, a challenge further complicated by the severe class imbalance often present in medical datasets. The research presented herein addresses these interconnected issues through a systematic, multi-stage analysis. An FL framework was implemented for cardiovascular risk prediction, where initial experiments showed that standard methods struggled with imbalanced data, resulting in a recall of zero. To overcome such a limitation, we first integrated the hybrid Synthetic Minority Over-sampling Technique with Tomek Links (SMOTETomek) at the client level, successfully developing a clinically useful model. Subsequently, the framework was optimized for non-IID data using a tuned FedProx algorithm. Our final results reveal a clear, non-linear trade-off between the privacy budget (epsilon) and model recall, with the optimized FedProx consistently out-performing standard FedAvg. An optimal operational region was identified on the privacy-utility frontier, where strong privacy guarantees (with epsilon 9.0) can be achieved while maintaining high clinical utility (recall greater than 77%). Ultimately, our study provides a practical methodological blueprint for creating effective, secure, and accurate diagnostic tools that can be applied to real-world, heterogeneous healthcare data.