Trajectory data, which capture the movement patterns of people and vehicles over time and space, are crucial for applications like traffic optimization and urban planning. However, issues such as noise and incompleteness often compromise data quality, leading to inaccurate trajectory analyses and limiting the potential of these applications. While Trajectory Data Preparation (TDP) can enhance data quality, existing methods suffer from two key limitations: (i) they do not address data privacy concerns, particularly in federated settings where trajectory data sharing is prohibited, and (ii) they typically design task-specific models that lack generalizability across diverse TDP scenarios. To overcome these challenges, we propose FedTDP, a privacy-preserving and unified framework that leverages the capabilities of Large Language Models (LLMs) for TDP in federated environments. Specifically, we: (i) design a trajectory privacy autoencoder to secure data transmission and protect privacy, (ii) introduce a trajectory knowledge enhancer to improve model learning of TDP-related knowledge, enabling the development of TDP-oriented LLMs, and (iii) propose federated parallel optimization to enhance training efficiency by reducing data transmission and enabling parallel model training. Experiments on 6 real datasets and 10 mainstream TDP tasks demonstrate that FedTDP consistently outperforms 13 state-of-the-art baselines.