When moving the drawing window from the primary display to a secondary monitor all drawing and tool functions stop working. It appears that on MacOS, Sketchup only works on the primary monitor. If you change the primary to one of the other attached monitors, SketchUp functions normally.
There are Many users who employ multiple monitor setups on Mac, I use a three monitor setup with SketchUp and Layout on Mac and do not experience any problems switching. How is your external monitor connected? When you drag the modeling window over to a new monitor the toolbars stay behind on the primary, and the window in the new monitor does not work? What if you open SketchUp fresh from the dock in your external monitor? Does the menu bar for SketchUp switch to the new monitor? Does it work? What kind of Mac are you using and what OS?