I looked at the two images. Are you using one or multiple focus points? The first one looks like the hand is in best focus. The second one looks great.
I think part of your blur problem is coming from shutter speed being too slow.
Shutter stops motion or shows motion. If your shutter is open for a long time you can move, the subject can move... That movement is recorded in the photograph as blur. If the shutter is only open for a very short time there isn't time enough for you to shake or the child to move.
A few rules to START with...
Your shutter speed should be equal to or greater than the reciprocal length of your lens. In many instances it should be twice as much. So if you have a 200mm lens your shutter speed should be more than 1/200 or if you are not the steadiest hand (most of us) more than 1/400. That is just to prevent blur from you shaking or moving the camera a slight bit.
Hand held photographing a still life your shutter speed should be equal to the above or more than about 1/80.
Hand held photographing a live subject your shutter should be above 1/125
Photographing a moving subject like a toddler above 1/250
For most sports I am at or above 1/400.
I think we touched on shutter priority mode earlier in the post. For now, try that out with those minimum shutter speeds. That will let the camera choose the aperture. If your camera has auto ISO you CAN let it choose, however I don't care for AUTO ISO. SO... if you aren't using auto ISO and your settings are blinking at you when you look at the viewfinder to take a shot it is telling you that it needs more light-you have to raise the ISO until it can get good exposure and stops blinking.
I'd guess that would be your first lesson in exposure! Shutter speed! Next comes learning about Aperture and Aperture Priority mode. A LOT of photographers prefer Aperture priority. I am not sure why they always default to that instead of Shutter Priority in shoots that shutter speed is your largest priority-but then I am not really very good in either priority mode and I shoot full manual (NOT what most do) all of the time. The ladies and gentlemen here can explain to you why that choice is.
When you are comfortable understanding Shutter Priority and to watch your settings start asking and someone will help you move on to controlling things with aperture and aperture priority.