I know that when I connect external display (it's a desktop computer, not a laptop), you get an enhanced menu with more options.
The TouchPortal launch icon is anchored in the corner of whatever screen is designated the primary, so can't drag and drop.
I don't need a virtual desktop. What I needed was a way to make TouchPortal anchor on the secondary screen, rather than the main one. I ended up getting UltraMon, so can switch which screen is the primary with a click of the mouse. Not a perfect solution, but it seems to be the only thing to do.
Thank you for your assist, though. Much appreciated.