Rotating a Camera with other objects

Should I be able to select objects and a camera (when Shown, of course) and rotate (or otherwise move) them all together? I’m finding that the camera doesn’t move though all its points are selected.

Actually it moves, but it won’t rotate.

This may or may not be related, but after attempting to edit the camera’s position by moving its points, the camera’s handles moved into an anomalous location without moving the camera’s position - shown below. This resets by toggling the camera, but snaps into existence after attempting to move it. This seems like a problem.

Hello - better, I think, to save a named view, then show the camera widget and manipulate that.