Running desktop software as a "service"
Go get Firedaemon (won't post the link, but it's a well known tool, just google it).
Set up your application to run as a new Firedaemon service (which will create a Windows service) and set it as interactive with the desktop and to run as that particular user.
When you or another admin logs on via RDP you can view what is going on but opening Firedaemon and right clicking that service and choosing to view Session 0. That will show you that "desktop" and the Quickbooks app.
Hope that helps.