Thanks for the additional details.
I understand better now.
A couple features that may help. First, the control points are by default when annotations, curves or light object sis picked.
This is where can control this setting, in case you have turned it off.
First select the leader object. To pick both control points, use a “window select” by first picking away from any geometry (1), and move cursor right up or down and pick the 2nd (2). Next move the points to the new location. (Of course, you can pick all or any combination of control points.)
If you have the Gumball on, it can help with the move, otherwise you can just drag the points at the same time.
Mary Ann Fugier
McNeel Technical Support and Training