To address the lack of physical interpretability in existing data-driven vehicle dynamics models which limits their generalization performance under extreme handling conditions and makes them susceptible to fitting distortion and long-term prediction divergence， this paper proposes a conditional multi-expert Koopman （CME-Koopman） network incorporating spectral stability regularization. Architecturally， the network introduces a condition-aware gating mechanism that dynamically dispatches multiple local linear Koopman expert models based on real-time vehicle operating conditions， thereby effectively characterizing the dynamic evolution of the vehicle from the linear handling region to the nonlinear saturation region. To mitigate the inherent instability of multi-step predictions， a spectral stability regularization term based on the power iteration method is introduced into the loss function. By explicitly constraining the modulus of the Koopman operator’s eigenvalues， this approach theoretically guarantees the boundedness and asymptotic stability of long-term predictions. Experiments conducted on the CarSim high-fidelity simulation platform demonstrate that， on a dataset containing 40% extreme handling conditions， the proposed method achieves a substantial reduction in long-term prediction error， namely root mean square error （RMSE） compared to the traditional deep extended dynamic mode decomposition （Deep EDMD） baseline. Furthermore， it accurately reproduces the asymptotic convergence characteristics of the vehicle at the critical point of instability. Closed-loop co-simulation with a model predictive controller （MPC） further validates the model’s engineering potential in extreme environments： It not only achieves high-precision trajectory tracking under strongly coupled longitudinal and lateral variable conditions， but also provides precise prediction of dynamics for the control system during sudden drops in road adhesion coefficient （μ-Jump）. This demonstrates its outstanding anti-divergence robustness and extreme sideslip prevention capabilities.