In-car navigation systems face challenges in ensuring safety while preserving data privacy. This paper proposes PrivNav, a federated learning scheme integrating differential privacy and secure multi-party computation for privacy-preserving learning. PrivNav enables vehicles to collaboratively train a model by aggregating locally computed updates without sharing raw data. Perturbations and secret sharing protect sensitive information and prevent inference attacks. PrivNav outperforms existing federated learning schemes by accommodating user dropouts, supporting customizable aggregation methods beyond FedAvg, and extending to decentralized scenarios without a trusted authority. Experiments demonstrate PrivNav's strong privacy guarantees and high accuracy, significantly enhancing the detection and control capabilities of in-car navigation safety systems. Precise event detection, abnormal situation differentiation, and reduced false alarms are achieved, improving overall system safety, trust, and performance.