To address the degradation of trajectory-tracking performance of Mecanum-wheeled omnidirectional vehicles caused by nominal inversion mismatch, wheel-end disturbances, body-level disturbances, and variations in reference speed, a dual-layer composite anti-disturbance trajectory-tracking method based on the U-model is proposed. First, a reference-shaping outer loop is constructed at the body level, where the desired body velocity is pre-corrected according to the pose error and velocity-tracking error and then allocated to wheel-end reference signals. Second, a wheel-end control inner loop with U-model-based dynamic inversion as the nominal control channel is constructed to realize nominal closed-loop shaping. Furthermore, a residual Super-Twisting second-order sliding-mode compensation law is designed and integrated with wheel-end disturbance-observer-based feedforward compensation to attenuate nominal inversion mismatch, modeling errors, and composite disturbances online. Comparative simulations under benchmark tracking, line--curve combined-trajectory tracking, composite disturbances, piecewise variable-speed conditions, and variable-speed conditions with input saturation are carried out on the MATLAB/Simulink platform. The results show that the proposed method achieves satisfactory tracking accuracy, disturbance rejection, and accuracy-retention performance under complex operating conditions.