Colorectal cancer (CRC) grading is a critical prognostic factor but remains hampered by inter-observer variability and the privacy constraints of multi-institutional data sharing. While deep learning offers a path to automation, centralized training models conflict with data governance regulations and neglect the diagnostic importance of multi-scale analysis. In this work, we propose a scalable, privacy-preserving federated learning (FL) framework for CRC histopathological grading that integrates multi-scale feature learning within a distributed training paradigm. Our approach employs a dual-stream ResNetRS50 backbone to concurrently capture fine-grained nuclear detail and broader tissue-level context. This architecture is integrated into a robust FL system stabilized using FedProx to mitigate client drift across heterogeneous data distributions from multiple hospitals. Extensive evaluation on the CRC-HGD dataset demonstrates that our framework achieves an overall accuracy of 83.5%, outperforming a comparable centralized model (81.6%). Crucially, the system excels in identifying the most aggressive Grade III tumors with a high recall of 87.5%, a key clinical priority to prevent dangerous false negatives. Performance further improves with higher magnification, reaching 88.0% accuracy at 40x. These results validate that our federated multi-scale approach not only preserves patient privacy but also enhances model performance and generalization. The proposed modular pipeline, with built-in preprocessing, checkpointing, and error handling, establishes a foundational step toward deployable, privacy-aware clinical AI for digital pathology.