We present a theoretical study of a new class of polymer materials of much recent experimental interest: polymer networks bearing dendritic wedges in the middle of long network strands. We focus on the Rouse dynamics of such cross-linked polymers and perform our study in three steps, considering first single dendritic wedges, then linear chains bearing dendritic wedges (CBDWs), and finally networks formed by end-linked CBDWs. Using analytical and numerical calculations we find that for linear CBDWs increasing the generation number g of dangling dendritic wedges decreases the storage shear modulus G'(omega) in the low-frequency domain, i.e., makes the large-scale relaxation more rapid. The zero shear viscosity also decreases with g, indicating a trend opposite to that of dendrimers with small g. Our findings are in qualitative agreement with recent rheological experimental data on side chain dendritic polymers. On the contrary, increasing g for dendritic wedges attached to regular networks slows down the low-frequency relaxation; this goes so far as to lead for large g in the intermediate frequency domain to a tendency toward a plateau in G'(omega). We relate these effects to the presence in CBDW systems' of the dangling dendritic wedges, which lower the mobility of the linear chains.