The dynamics of the distorted cholesteric director is studied in a complex matrix, such as mesogenic and istotropic polymer networks, by means of dynamic light scattering. We employ polymer-stabilized cholesteric diffraction gratings as our system to measure thermal fluctuations of the cholesteric director in photostabilized low-molecular-weight polymer networks. The relaxation rates of fast and slow dynamical modes of the distorted cholesteric directors are measured in two scattering geometries, where the scattering vector is either parallel or perpendicular to the helical axis. The dispersion relations for fluctuation wave vectors along the helical axis are found to be fundamentally different for the two types of polymer networks. Experimental dispersion curves are in agreement with the theoretical predictions developed in the present paper. A possible understanding of dispersion in distorted cholesterics is developed and the experimental results for polymer stabilized cholesteric diffraction gratings are presented in this report. We also discuss the coupling of a slow relaxation mode of distorted cholesterics in a mesogenic versus isotropic polymer network.