The advancement of Autonomous Vehicles (AVs) has led to a need for scheduling computational tasks generated by dynamically arriving mixed-criticality functions on vehicular heterogeneous processing platform. However, the existing scheduling methods cannot deal with the complex characteristics of function system on Intelligent Driving Operating System (IDOS), and guarantee system reliability and efficiency among various traffic environments. This paper proposes a novel Laxity-Driven Reliable Dynamic Scheduling (LD-RDS) for IDOS, aiming to improve system reliability in terms of maximizing Deadline Satisfaction Ratio (DSR). Specifically, LD-RDS constructs adaptive laxity to prioritize exigent tasks, and sorts tasks considering criticality and exigency comprehensively. Experimental results show that our method provides a significant improvement in terms of both reliability and efficiency, in particular, with an increase of 43.7% in function deadline satisfaction ratio and a reduction of 23.0% in completion time consumption on average, compared to several baselines under the demanding scenarios.