This paper introduces a novel resource-efficient control structure for remote path-following control of autonomous vehicles based on a comprehensive combination of Kalman filtering, non-uniform dual-rate sampling, periodic event-triggered communication, and prediction-based and packet-based control techniques. An essential component of the control solution is a non-uniform dual-rate extended Kalman filter (NUDREKF), which includes an h-step ahead prediction stage. The prediction error of the NUDREKF is ensured to be exponentially mean-square bounded. The algorithmic implementation of the filter is straightforward and triggered by periodic event conditions. The main goal of the approach is to achieve efficient usage of resources in a wireless networked control system (WNCS), while maintaining satisfactory path-following behavior for the vehicle (a holonomic Mecanum-wheeled robot). The proposal is additionally capable of coping with typical drawbacks of WNCS such as time-varying delays, and packet dropouts and disorder. A Simscape Multibody simulation application reveals reductions of up to 93% in resource usage compared to a nominal time-triggered control solution. The simulation results are experimentally validated in the holonomic Mecanum-wheeled robotic platform.