From an integrated motor-robot perspective, this paper addresses the problem of global predefined-time trajectory tracking control for a four-wheel independent drive skid-steering robot (FWID-SSMR) under prescribed performance constraints. Unlike previous studies that focus solely on kinematic or dynamic models, this paper presents an integrated dynamic model for FWID-SSMR with consideration of parameter variations, frictional resistance, external disturbances, wheel slip, unknown failure, and motor saturation during operation, which comprehensively describes the kinematics, dynamics, and wheel dynamics (including motor drive dynamics and wheel slip) of the FWID-SSMR. Based on this model, an adaptive hierarchical global predefined-time performance constraints control scheme is developed, comprising trajectory tracking control, control allocation strategy, and motor drive control. These three interconnected mechanisms are collaboratively optimized to achieve flexible, designer-specified tracking performance indicators, including settling time, overshoot, convergence speed, and steady-state error. This control scheme achieves global prescribed performance control and overcomes the dependency of settling time on initial conditions. Theoretical analysis and simulation results jointly validate the effectiveness and superiority of the developed control scheme in trajectory tracking of FWID-SSMR.