Driver distraction remains a leading cause of traffic accidents, making its recognition critical for enhancing road safety. In this paper, we propose a novel method that combines the Information Bottleneck (IB) theory with Graph Convolutional Networks (GCNs) to address the challenge of driver distraction recognition. Our approach introduces a 2D pose estimation-based action recognition network that effectively enhances the retention of relevant information within neural networks, compensating for the limited data typically available in real-world driving scenarios. The network is further refined by integrating the CTR-GCN (Channel-wise Topology Refinement Graph Convolutional Network), which models the dynamic spatial-temporal relationships of human skeletal data. This enables precise detection of distraction behaviors, such as using a mobile phone, drinking water, or adjusting in-vehicle controls, even under constrained input conditions. The IB theory is applied to optimize the trade-off between information compression and task-relevant feature retention, allowing the model to focus on the most critical data for action classification. Comprehensive experiments conducted on the NTU-RGB+D and KIT Drive&Act datasets demonstrate that the proposed method outperforms existing approaches in terms of accuracy, especially when dealing with limited or incomplete input data. Additionally, a custom D1-DDB dataset was created, featuring 21 distinct driver behaviors, including both normal and distracted actions. The model successfully recognizes these behaviors with a high degree of accuracy, showcasing its robustness and adaptability in various driving environments.