The development and validation of lateral control strategies for railway running gears with independently rotating driven wheels (IRDWs) are an active research area due to their potential to enhance straight-track centering, curve steering performance, and reduce noise and wheel–rail wear. This paper focuses on the practical application of theoretical models to a 1:5 scaled test rig developed by the German Aerospace Center (DLR), addressing the challenges posed by unmodeled phenomena such as hysteresis, varying damping and parameter identification. The theoretical model from prior work is adapted based on empirical measurements from the test rig, incorporating the varying open-loop stability of the front and rear wheel carriers, hysteresis effects, and other dynamic properties typically neglected in literature. A transparent procedure for identifying dynamic parameters is developed, validated through closed- and open-loop measurements. The refined model informs the design and tuning of a cascaded PI and PD controller, enhancing system stabilization by compensating for hysteresis and damping variations. The proposed approach demonstrates improved robustness and performance in controlling the lateral displacement of IRDWs, contributing to the advancement of safety-critical railway technologies.