Data-driven inertial sequence learning has revolutionized navigation in GPS-denied environments, offering superior odometric resolution compared to traditional Bayesian methods. However, deep learning-based inertial tracking systems remain vulnerable to privacy breaches that can expose sensitive training data. \hl{Existing differential privacy solutions often compromise model performance by introducing excessive noise, particularly in high-frequency inertial measurements.} In this article, we propose ConvXformer, a hybrid architecture that fuses ConvNeXt blocks with Transformer encoders in a hierarchical structure for robust inertial navigation. We propose an efficient differential privacy mechanism incorporating adaptive gradient clipping and gradient-aligned noise injection (GANI) to protect sensitive information while ensuring model performance. Our framework leverages truncated singular value decomposition for gradient processing, enabling precise control over the privacy-utility trade-off. Comprehensive performance evaluations on benchmark datasets (OxIOD, RIDI, RoNIN) demonstrate that ConvXformer surpasses state-of-the-art methods, achieving more than 40% improvement in positioning accuracy while ensuring $(ε,δ)$-differential privacy guarantees. To validate real-world performance, we introduce the Mech-IO dataset, collected from the mechanical engineering building at KAIST, where intense magnetic fields from industrial equipment induce significant sensor perturbations. This demonstrated robustness under severe environmental distortions makes our framework well-suited for secure and intelligent navigation in cyber-physical systems.