We present evidence for kinematically decoupled cores (KDCs) in two dwarf early-type (dE) galaxies in the Virgo cluster, VCC 1183 and VCC 1453, studied as part of the SMAKCED stellar absorption-line spectroscopy and imaging survey. These KDCs have radii of 1.''8 (0.14 kpc) and 4.''2 (0.33 kpc), respectively. Each of these KDCs is distinct from the main body of its host galaxy in two ways: (1) inverted sense of rotation and (2) younger (and possibly more metal-rich) stellar population. The observed stellar population differences are probably associated with the KDC, although we cannot rule out the possibility of intrinsic radial gradients in the host galaxy. We describe a statistical analysis method to detect, quantify the significance of, and characterize KDCs in long-slit rotation curve data. We apply this method to the two dE galaxies presented in this paper and to five other dEs for which KDCs have been reported in the literature. Among these seven dEs, there are four significant KDC detections, two marginal KDC detections, and one dE with an unusual central kinematic anomaly that may be an asymmetric KDC. The frequency of occurrence of KDCs and their properties provide important constraints on the formation history of their host galaxies. We discuss different formation scenarios for these KDCs in cluster environments and find that dwarf-dwarf wet mergers or gas accretion can explain the properties of these KDCs. Both of these mechanisms require that the progenitor had a close companion with a low relative velocity. This suggests that KDCs were formed in galaxy pairs residing in a poor group environment or in isolation whose subsequent infall into the cluster quenched star formation.