Federated fine-tuning has emerged as a promising approach for adapting foundation models (FMs) to diverse downstream tasks in edge environments. In Internet of Vehicles (IoV) systems, enabling efficient and low-latency multi-task adaptation is particularly challenging due to client mobility, heterogeneous resources, and intermittent connectivity. This paper proposes a hierarchical federated fine-tuning framework that coordinates roadside units (RSUs) and vehicles to support resource-aware and mobility-resilient learning across dynamic IoV scenarios. Leveraging Low-Rank Adaptation (LoRA), we introduce a decentralized, energy-aware rank adaptation mechanism formulated as a constrained multi-armed bandit problem. A novel UCB-DUAL algorithm is developed to enable adaptive exploration under per-task energy budgets, achieving provable sublinear regret. To evaluate our method, we construct a large-scale IoV simulator based on real-world trajectories, capturing dynamic participation, RSU handoffs, and communication variability. Extensive experiments show that our approach achieves the best accuracy-efficiency trade-off among all baselines, reducing latency by over 24\% and improving average accuracy by more than 2.5\%.

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