My Nvidia card comes with something called GeForce Experience. Not only will it record video, but you can even upload directly to FB and YT from the app. As for undocking, are you talking about windowed mode or something else. If you're looking to take the in-flight UI windows to a second monitor, then click the highlighted button and they'll undock in either windowed or full-screen mode.
I have shadowplay for recording......I'm talking about FSrecorder there, the app that lets you playback and fly with yourself and create different camera views sadly discontinued after FSX but anyone with FS9/FSX would say its an essential
Will check out the undocking to a second monitior although I think thats only instruments....I'm after cockpit view on one screen and Chase plane on the opther for video clips