Thanks for updating your post with your further findings. We do not allow multi-selections across different parents when single selecting or selecting in the tree. However this can be done with the selection rectangle. If you use the selection rectangle you could select two objects from different groups. Then the arrow keys would work to move the two groups.
By selection rectangle I mean this method of selecting objects: Using your mouse, draw a rectangle within your work area by clicking, and while holding down the left mouse button, dragging the cursor to define a rectangle. All objects within the rectangle will be selected.
Why we don’t allow single selecting across parents is another issue. I will write an issue to do some investigation about how we can make this better.