This paper aims to enhance the performance of Vehicular Platooning (VP) systems integrated with Wireless Federated Learning (WFL). In highly dynamic environments, vehicular platoons experience frequent communication changes and resource constraints, which significantly affect information exchange and learning model synchronization. To address these challenges, we first formulate WFL in VP as a joint optimization problem that simultaneously considers Age of Information (AoI) and Federated Learning Model Drift (FLMD) to ensure timely and accurate control. Through theoretical analysis, we examine the impact of FLMD on convergence performance and develop a two-stage Resource-Aware Control framework (RACE). The first stage employs a Lagrangian dual decomposition method for resource configuration, while the second stage implements a multi-agent deep reinforcement learning approach for vehicle selection. The approach integrates Multi-Head Self-Attention and Long Short-Term Memory networks to capture spatiotemporal correlations in communication states. Experimental results demonstrate that, compared to baseline methods, the proposed framework improves AoI optimization by up to 45%, accelerates learning convergence, and adapts more effectively to dynamic VP environments on the AI4MARS dataset.