I cannot get it to work with either a trackpad or a mouse. I can drag to get to left/right screen and that works with both trackpad and mouse, but I can’t drag to get to Message Center or Control Center. Has anybody else managed?
I use Mirroring occasionally. I’m not sure what you mean by “Message Center,” but I can say that accessing Control Center by swiping down from the top-right does not work for me either. I can swipe left and right (as you said). And none of the View menu shortcuts get you there either. Guess it’s not available on Mirroring 
The thing you get when you swipe from the top center down.
Ahh. Nope, no vertical swiping from anywhere.
4 posts were split to a new topic: How do you use iPhone Mirroring on your Mac?
I know that I can click the Home Bar (rather than drag from the bottom) to go home (well, plus Cmd-1, or click the icon on the window bar top-right when you hover over the top), so I was hoping that a mere click on the top-left for notification center or top-right for control panel would work - but no such luck. Web searching revealed that you are not the first one to find that these are not accessible in iPhone Mirroring.
FWIW, Cmd-2 reveals the App Switcher, Cmd-3 launches spotlight search.
I was aware of those and hoping to find something similar for Control and Message Center. But so far no luck. It appears those shortcuts exist because these are the ones Apple considered important enough to assign their own keyboard/toolbar shortcuts. It appears as if it’s not one of those, no luck. :( I’m still hoping one of the smart people here has figured out something that works.
I wonder if perhaps Accessibility would allow setting something up instead of the swipe.
And as I think about that it occurs to me that iPhone Mirroring also likely won’t provide for a way for folks to get at whatever they usually do with double and triple back taps.
No. 
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