This paper addresses the problem of lateral dynamics estimation of a vehicle and critical situations detection. For this purpose, two cascaded unknown input observers are designed which achieve finite time convergence. The system describing the lateral vehicle dynamics is decomposed into two sub-systems which are described with linear parameter varying models (LPV) according to the longitudinal velocity. For each sub-system, an unknown input observer is designed by the use of the relative degree of the considered unknown inputs with respect to the outputs. Theoretically, the observers are designed to ensure, firstly, asymptotic state estimation error convergence and secondly, finite time convergence by the use of the geometric homogeneity concept. A strategy for critical situations detection is presented by comparing the estimated nonlinear forces to the linear version obtained from a linear model of the forces and the estimated lateral velocity. Simulation results are provided to illustrate the proposed observer structure and the critical situations detection.