i'm dealing with the same issue
MBP 16" + 27" monitor on my desk, and the need to control it via remote desktop
Remote desktop is not easy to use with multiple monitor (you see only one at a time, you can't drag and drop between screens, you can't move windows between screens, etc)
Turning on miroring is a solution but i really would like to find a way to disable the external monitor
One solution, a weird one but i have no other solution at the moment, is to plug the monitor to a remote controlled electric plug, and to switch on/off this plug via an app wich can be scripted (a one clic solution)
It cost 5 to 10$ (or €) and a bit of work to make it "one-clic"
There can be some issue : the wifi need to be live, the plug need to work without bug, and some monitors need a physical press on their "power" button to wake-up
Maybe i'll try that one day