We report evidence for dynamically significant rotation in the globular cluster systems of two luminous Virgo dwarf ellipticals, VCC1261 and VCC1528. Including previous results for VCC1087, the globular cluster systems of all three Virgo dwarf ellipticals studied in detail to date exhibit v_rot/sigma > 1. Taking the rotation seen in the globular clusters as a maximal disk rotation, and accounting for the possible fading of any hypothetical progenitor galaxy, we find all three dEs lie on the r-band Tully-Fisher relation. We argue that these data support the hypothesis that luminous dEs are the remnants of transformed disk galaxies. Based on the GC kinematics, we find tentative evidence for nonbaryonic mass to light ratios at the largest galactocentric radii (4-7 effective radii, depending upon the galaxy). We also obtained deep, longslit data for the stars in VCC1261 and VCC1528. Both these galaxies show rapid rotation in their inner regions, with spatial scales of ~0.5 kpc. These rotation velocities are surprisingly similar to those seen in the GC systems. At larger radii, we see little rotation in the dEs themselves. Since our longslit data for Virgo dEs extend out to 1-2 effective radii (typical of deep observations), whereas the globular clusters extend out to 4-7 effective radii, we conclude that non-detections of rotation in many luminous dEs may simply be due to a lack of radial coverage in the stellar data, and that globular clusters represent singularly sensitive probes of the dynamics of dEs. Based on these data, we suggest that gas disks are significant sites of globular cluster formation in the early universe.