Obstacle avoidance in human-machine shared control vehicles under complex conditions presents a significant challenge. This paper proposes a novel adaptive nonlinear stochastic cooperative game control strategy to enhance the safety and stability on low-adhesion surfaces, accounting for the nonlinear dynamics of vehicles and the uncertainties of heterogeneous drivers. Firstly, a nonlinear vehicle-driver model is established, considering both nonlinear tire dynamics and uncertainties associated with driver behavior on low-adhesion surfaces. To facilitate the solution of the nonlinear game optimization problem, the model is linearized utilizing piecewise affine theory. Subsequently, a human-machine dynamic interaction model is constructed based on nonlinear stochastic game theory. To enable adaptive cooperative control within this game interaction framework, a hierarchical adaptive weight distribution strategy is proposed. This strategy integrates a fuzzy control method that considers multiple factors, along with a constrained optimization approach to dynamically adjust the weight coefficient. Based on the interaction model and adaptive distribution strategy, the dynamic interaction problem is reformulated as a coupled quadratic programming problem with probabilistic safety constraints. Convex iteration and probabilistic constraint tightening methods are employed to derive the Pareto optimal solution for vehicle safety control. Hardware-in-the-loop simulation results demonstrate that the proposed control strategy facilitates dynamic cooperative control between the driver with behavioral uncertainty and the automation system across various scenarios. Compared to the baseline methods, the proposed approach improves the vehicle's stability and safety.