I have the latest DF beta installed on Windows 7, but my issue has existed since well before that. I have 2 monitors, each of which has a different set of icons on its desktop (and taskbars). I like to sort them alphabetically, especially when installing a new program. Sometimes when a program is installed by either user or all users, it can't be alphabetized like the others. I need to cut the icon from the desktop and paste into the "Desktop" folder of file explorer. This works fine for the primary desktop, but not for the 2nd monitor.

Is there a way to cut and paste icons within the secondary monitor exclusively?

Dragging icons between monitors isn't the problem, it's the sorting by name. But I figured out if I cut them and paste to desktop folder in explorer, everything works out fine. I guess I solved my own problem!