This will sound infinitely stupid, probably... am I understanding this correctly(?)... If I undock my library (I assume that means undock it from the GUI so it floats and can be moved around), then it uses Adobe AIR to access the library content... but if I leave it docked, it uses Flash to access content libraries?

I never undock it... I may have accidentally moved it top the top (switched positions with the parameters windows)... but I never undock it... 

Flash is as up to date as my OS will allow, and aside from the installer and uninstallers for Adobe AIR which I can find in my Utilities folder, I see no other way to access AIR... I did a software update check, but the computer claims everthing is up to date.

That being said, I see no obvious way to choose a library... 

The General Prefs menu is not giving me a choice...