As models for inhomogeneous polymer networks, we investigate the Rouse dynamics of regular lattices built from subunits with arbitrary internal structure. We analyze as an example a two-dimensional lattice, consisting of small-world networks (SWNs). Using analytical and numerical calculations we study the stretching of such a structure under an external force. We find that the network shows interesting relaxation features and an unusual behavior in the intermediate time (frequency) domain, which lies in the region between the modes of the SWN subunits and those of the lattice. This behavior is related to the SWN-density of states, which leads to the appearance of a "pseudogap" between the highest lattice eigenvalue and the lowest SWN eigenvalue.