A new hybrid moving grid approach to wave packet dynamics is described. Exterior points within a nonrigid frame follow Lagrangian trajectories obtained by solving the hydrodynamic equations of motion. Internal grid points within one or more open windows follow non-Lagrangian adaptive paths. Within these windows, problems encountered with quantum trajectories near wave function nodes are circumvented by directly solving the moving path transform of the Schrodinger equation. Excellent results are obtained for evolution of the density in a double well potential even though multiple ripples develop in the density.