We present the dynamical analysis of a sample of 12 dwarf elliptical (dE) galaxies for which we have obtained SAURON large-scale two-dimensional spectroscopic data. We construct Jeans axisymmetric models and obtain total dynamical masses enclosed within one effective radius. We use the obtained values to show that the validity of the dynamical scaling relations of massive early-type galaxies can be extended to these low-mass systems, except that dEs seem to contain relatively larger fraction of dark matter in their inner parts. We then demonstrate that dE galaxies have lower angular momenta than the present-day analogues of their presumed late-type progenitors, and we show that dE circular velocity curves are steeper than the rotation curves of galaxies with equal and up to an order of magnitude higher luminosity. This requires a transformation mechanism that is not only able to lower the angular momentum but also one that needs to account for increased stellar concentration. Additionally, we match the dark matter fraction of our galaxies to their location in the Virgo Cluster and see that galaxies in the cluster outskirts tend to have a higher dark-to-stellar matter ratio. Transformation due to tidal harassment is able to explain all of the above, unless the dE progenitors were already compact and had lower angular momenta at higher redshifts.