That is because you glitched your mouse cursor into Blockland. Whenever you move the mouse it jerks around the middle. Not just because of the Flying Wheeled Jeep.
You're not supposed to have your mouse cursor in blockland, try clicking M to disable it
Uncheck "Show mouse" option before you're recording. When you're recording with it on, it can see the mouse, even if you can't.You'll see the same thing if you go into any FPS game.