In emergency circumstances, it is essential for autonomous vehicles to balance stability and dynamic performance to attain a faster travel speed while preserving stability. It is not unusual to find traffic accidents caused by suddenly present intruders on the road. In this situation, if there is not enough distance for the vehicle to brake immediately, the vehicle needs to operate with a relatively big steering angle and cornering speed to avoid collision while maintaining driving stability. This can be a challenging scenario even for a human driver, let alone autonomous driving. Especially, this poses a burden on trajectory optimization. In this case, neither over-conservative nor unachievable trajectory and speed profiles are eligible. Technically, the difficulty lies in an accurate maximum cornering speed estimation due to the impact of nonlinear tire force responses in these scenarios with large steering angles and high cornering speed. While this difficulty can be addressed by introducing tire model and extra variables, like tire stiffness and shape factor, in the formulation of this problem to cover nonlinear effect, it ends up increasing the complexity of the model and optimization problem. In this paper, a novel maximum curve-passing speed correction method for online trajectory optimization is proposed by leveraging predefined nonlinear correction terms, which is applicable without introducing any extra variables to the optimization. Moreover, this method has been simulated in the autonomous vehicle software-in-the-loop system. It is validated that this method can achieve online trajectory planning with maximum curve-passing speed while ensuring lateral stability.