<p>Slope driving of autonomous vehicles faces significant challenges in simultaneously achieving accurate path-tracking and maintaining lateral stability. To overcome these limitations, a cooperative control framework is presented that integrates a computationally efficient region of attraction (RoA) estimation with an adaptive output feedback distributed model predictive control (DMPC) strategy. The vehicle stability RoA is obtained from the sum-of-squares programming (SoSP) method. To reduce fitting complexity while maintaining accuracy, the polynomial parameters of the RoA are simplified. A stability coefficient is then derived from a radial basis function neural network (RBFNN) trained with simulation data to represent the real-time stability state of the vehicle. Based on the stability coefficient, the DMPC strategy is developed to coordinate the control of active front steering, active rear steering, and direct yaw moment. The weight of direct yaw moment is adjusted online and further refined through an adaptive tuning mechanism, which overcomes the convergence limitations of integral-based MPC by dynamically updating the stability coefficient according to output variation. Simulation experiments conducted in uphill and downhill cornering scenarios indicate that the proposed method significantly improves path-tracking accuracy and lateral stability, and effectively mitigates coordination conflicts among the chassis subsystems. Specifically, compared with other given baseline strategies, the lateral displacement errors are reduced by 39.69% and 54.02%, respectively, and the lateral velocity errors are reduced by 30.05% and 44.43%, respectively.</p>