We formally discuss a numerical approach for the simulation of a highly nonlinear two-dimensional model for immiscible incompressible two-phase flows in heterogeneous porous media to deal with dynamic capillary pressure. Hybridized  mixed finite elements and domain decomposition procedures are used for the spatial discretization of the equations. Proper locally conservative finite volume techniques are used for a balancing discretization of the first-order hyperbolic flux and the dispersive behavior inherent of the pseudo-parabolic model. Our numerical experiments confirm the viability of the proposed formulation based on computational simulations subject to high-contrast heterogeneous porous media nonlinear flows.