This paper proposes a new integrated vehicle dynamics management for enhancing the yaw stability and wheel slip regulation of the distributed-drive electric vehicle with active front steering. To cope with the unknown nonlinear tire dynamics with uncertain disturbances in integrated control problem of vehicle dynamics, a neuro-adaptive predictive control is therefore proposed for multiobjective coordination of constrained systems with unknown nonlinearity. Unknown nonlinearity with unmodeled dynamics is modeled using a random projection neural network via adaptive machine learning, where a new adaptation law is designed in premise of Lyapunov stability. Given the computational efficiency, a neurodynamic method is extended to solve the constrained programming problem with unknown nonlinearity. To test the performance of the proposed control method, simulations were conducted using a validated vehicle model. Simulation results show that the proposed neuro-adaptive predictive controller outperforms the classical model predictive controller in tracking nominal wheel slip ratio, desired vehicle yaw rate and sideslip angle, showing its significance in vehicle yaw stability enhancement and wheels slip regulation.