I bet you didn't try what I want to do, though! Yes, they both work simultaneously as pointing devices, but I can't spot where to separately set the button settings. Both are either RH or LH, not one of each.
Do Logitech or Kensington have software apps that let you control the button orientation independent of the Windows settings?
Not ones that I've found.
you can use autohotkey to disable the generic click from the "logical mouse" Windows is seeing and then capture the HID information yourself and send out the logical mouse click depending on which [hysical mouse's left or right click.
Other than Logitech Setpoint: Wireless Trackball M570 - Logitech Support
And Kensington TrackBallWorks: TrackballWorks™ Customization Software - Trackballs - Control - Products - Kensington