Take more pics and show us how you make out.
Some say a tripod is the next purchase before a second lens...and I do believe that, but with pics of your kids, I think a lens like marc pointed out would be my first choice.
For my kid shots..I set focus to AFC S (it focuses once only), and set the focus area to "Centre". I place my chlds face in the centre of the frame...press the shutter half way down and let it lock onto focus....the while still holding the shutter half way down I move the camera to where I want the shot to be. That way his face is always in focus. It's easier than it sounds.
good luck!
ps...if you find it getting easier.....have some fun with very old Pentax/Takumar lenses. I typically use lenses that are 40 or 50 years old and they make me look better than I am. More if a learning curve but my point is you have alot of fun ahead with your k20d.
Steve