Emergency scenarios may require trajectory planning at actuator and friction limits within tight obstacle constraints. This paper presents an approach to handle such scenarios using Linear Time Varying Model Predictive Control, in the presence of both static and dynamic obstacles. With the proposed approach, the controller transitions between a kinematic vehicle model, which is stable at low velocities, and a dynamic vehicle model, which is more accurate at high velocities, based on a threshold velocity. This ensures the functionality of the controller in emergency braking scenarios and enables manoeuvre initialization with a full braking trajectory. An adjustable safety distance concept is introduced that considers the criticality of the scenario and tightens or loosens the obstacle avoidance and friction constraints accordingly. Simulation results show that the controller is capable of handling various critical situations, including those when the vehicle comes to a stop at the end of a high speed evasive manoeuvre. Furthermore, it is more effective at keeping a safety distance from obstacles in such manoeuvres than by using fixed safety distance concept.