The increasing use of electronic health records (EHRs) has transformed healthcare management, yet data sharing across institutions remains limited due to privacy concerns. Federated learning (FL) offers a privacy-preserving solution by enabling collaborative model training without centralized data sharing. However, non-independent and identically distributed (non-IID) data distributions, where the data across clients differ in class proportions and feature characteristics, pose a major challenge to achieving robust model performance. In this study, we propose a hybrid framework that combines the Federated Proximal (FedProx) algorithm with the ResNet50 architecture to address non-IID data issues. We artificially partitioned an IID brain tumor dataset into non-IID subsets to simulate real-world conditions and applied data augmentation techniques to balance class distributions. Global model performance is monitored across 100 training rounds with varying regularization parameters in FedProx. The proposed framework achieved an accuracy of 97.71% on IID data and 87.19% in extreme non-IID scenarios, with precision, recall, and F1-scores also demonstrating strong performance. These findings highlight the effectiveness of combining data augmentation with FedProx in mitigating data imbalance in FL, thereby supporting equitable and efficient training of privacy-preserving models for healthcare applications.