Yep, motion blur is definitely the major problem there. There are a couple of causes, or rather, contributers…
- The focal length. (A longer focal length serves to amplify any camera shake that is present.)
- The slow-ish shutter speed. (There is a photography rule that says, “To eliminate motion blur, use a shutter speed equal to or greater than your focal length.”) So, if your focal length is set to 200mm, use a shutter speed of at least 1/200 sec, or more, (1/250, 1/320, or higher)
One thing that will help with getting a fast enough shutter speed and give you better OOF backgrounds, is to open up your aperture to your lens’s maximum of f/5.6 instead of stopping down to f/8. That will let you kill 2 birds with one stone! Less motion blur, and nicer, blurrier backgrounds!
As @JamesStaddon said, the 50mm will help with your slow shutter speed/motion blur problem, because you only need a shutter speed of 1/50 sec. Note that the focal length/shutter speed rule doesn’t take subject movement into consideration, so I would still keep it up around 1/100 just to be safe.