This is maybe more a difficulty between one's ears than any real limitation of Illustrator. Let's assume I should drag the selected star and square so that the midpoint of the square hits the top end of the red curve:

[![enter image description here][1]][1]

I simply take the direct selection tool (the normal selection tool changes temporarily to direct selection tool if one presses Ctrl) Then I drag the midpoint to the wanted place. It snaps if Smart Guides and Snap to Point are ON:

[![enter image description here][2]][2]

To apply the "drag whole selection by dragging one node" works if nothing is touched after making the selection. And for snapping there should be something in the target point which can be snapped to.

Your question was formulated to contain everything which possibly can be transformed, not only the place, which was used as an example. My answer for the general form is "do the transformation and do not care what happens to other selected items, watch only thi interesting part in the selection".


  [1]: https://i.sstatic.net/bFNPK.jpg
  [2]: https://i.sstatic.net/NTuGS.png