[Nick Sloan]

...or you could select all relevant tasks and press Reset in the task inspector: all subtasks will revert to as early as constraints allow, and should be draggable by group.

Actually kwispel I think you have hit upon a major conceptual shortcoming of OmniPlan: simply dragging a task bar converts it to start on a specific date. It is easy to suppose that by dragging tasks within a group you are setting up the temporal relationships between them, but you are not: you are setting each task to a specific date and in effect breaking the relationships, so that if the group bar is dragged, the previously dragged tasks do not move with it.

In order to establish relationships between tasks in a group without anchoring tasks to specific dates you have to use dependencies, and if you want a gap between tasks you have to specify a lead time in the Task/Dependencies inspector.

On the face of it OmniPlan seems to offer very direct and intuitive setting up of schedules by dragging, but in practice it is all too easy to tie yourself in knots by inadvertently assigning fixed dates. There are a couple of things which I think would help a lot:
1) Make dependency lines draggable, so that by dragging the arrowhead, lead times could be set up graphically.
2) Make groups modifier-draggable so that all (unlocked) tasks move in unison with the group task without changing their relationships.

I am not convinced by the logic that assigns specific dates to all dragged tasks (especially since constraints and locking are both available to tell OmniPlan: “hey, this task really has to start on or after this date”), but since that is the way OP works, at least it should be made possible for users to drag things around without upsetting relationships.