While highly automated driving relies most of the time on a smooth driving assumption, the possibility of a vehicle performing harsh maneuvers with high dynamic driving to face unexpected events is very likely. The modeling of the behavior of the vehicle in these events is crucial to proper planning and controlling; the used model should present accurate and computationally efficient properties to ensure consistency with the dynamics of the vehicle and to be employed in real-time systems. In this article, we propose an LSTM-based hybrid extended bicycle model able to present an accurate description of the state of the vehicle for both normal and aggressive situations. The introduced model is used in a Model Predictive Path Integral (MPPI) plan and control framework for performing trajectories in high-dynamic scenarios. The proposed model and framework prove their ability to plan feasible trajectories ensuring an accurate vehicle behavior even at the limits of handling.