We present a kinematic analysis of the globular cluster (GC) systems and diffuse stellar light of four intermediate luminosity (sub-L∗) early-type galaxies in the Virgo cluster based on Gemini Multi-Object Spectrographs (GMOS) data. Our galaxy sample is fainter () than most previous studies, nearly doubling the number of galaxies in this magnitude range that now have GC kinematics. The data for the diffuse light extends to 4Re, and the data for the GCs reaches 8-12Re. We find that the kinematics in these outer regions are all different despite the fact that these four galaxies have similar photometric properties, and are uniformly classified as "fast rotators" from their stellar kinematics within 1Re. The GC systems exhibit a wide range of kinematic morphology. The rotation axis and amplitude can change between the inner and outer regions, including a case of counter-rotation. This difference shows the importance of wide-field kinematic studies, and shows that stellar and GC kinematics can change significantly as one moves beyond the inner regions of galaxies. Moreover, the kinematics of the GC systems can differ from that of the stars, suggesting that the formation of the two populations are also distinct.