We present a novel grid-forming control design approach for dynamic virtual power plants (DVPP). We consider a group of heterogeneous grid-forming distributed energy resources which collectively provide desired dynamic ancillary services, such as fast frequency and voltage control, which no individual device can provide in isolation. To achieve that, we employ an adaptive divide-and-conquer strategy that disaggregates the desired control specifications of the aggregate DVPP via adaptive dynamic participation factors to obtain local desired behaviors of each device. We then employ local controls to realize these desired behaviors. In the process, physical and engineered limits of each device are taken into account. We extend the proposed approach to make it also compatible with grid-following device controls, thereby establishing the concept of so-called hybrid DVPPs. Further, we generalize the DVPP design to spatially dispersed device locations in power grids with different voltage levels. Finally, the DVPP control performance is verified via numerical case studies in the IEEE nine-bus transmission grid with an underlying medium voltage distribution grid.