In order to move more than one video clip at a time, select all of the desired layers in the Layers or Timeline panel. Then, in the Timeline panel, drag to reposition all clips. You can select clips from within a Video Group, across different Video Groups and/or any other layers in the document and move them – as long as the location that you’re trying to move them to doesn’t have other content (videos, stills etc.).
Note: To select multiple layers, Command (Mac) | Control (Win) -click the desired layers, or Shift -click to select a range of contiguous layers.

If I can understand correctly, here you say that selected layers (clips) can not be moved to the same line (Video Group) on Timeline if there are already stills or video clips. I just tried to ensure but layers and clips selected on Timeline or in Layers panel can be moved anywhere.