The rapid growth of autonomous driving in recent years has posed some new research challenges to the traditional vehicle control system. For example, in order to flexibly change the yaw rate and moving speed of a vehicle based on the detected road conditions, autonomous driving control often needs to dynamically tune its control parameters for better trajectory tracking and vehicle stability. Consequently, the execution time of driving control can increase significantly, resulting in missing the end-to-end (E2E) deadline from detection to computation and actuation, and thus possible accidents. In this paper, we propose AutoE2E, a two-tier real-time scheduling framework that helps the automotive OS meet the E2E deadlines of all the tasks despite execution time variations, while achieving the maximum possible computing precision for driving control. The inner loop of AutoE2E dynamically controls the CPU utilizations of all the on-board processors to stay below their respective schedulable utilization bounds, by adjusting the invocation rates of the vehicle control tasks running on those processors. The outer loop is designed to adapt the computation time of driving control and minimize the precision loss, when the inner loop loses its control capability due to rate saturation caused by vehicle speed changes. In particular, the outer loop features driver-oriented weight assignment and piecewise approximation for computing precision optimization of vehicle control tasks. Our evaluations, both on a hardware testbed with scaled cars and in larger-scale simulation, show that AutoE2E can effectively reduce the deadline miss ratio by 35.4% on average, compared to well-designed baselines, while having smaller precision loss and tracking errors.