Jonathan.
Your samples look completely OOF to me. Just entirely missed focus point. If it were me, I would select just the center focus point. Turn all the others off. As a matter of fact I rarely use anything but the single, center point focus. Focus on the eye.
Use One Shot, not AI-Servo.
Also it could be camera shake because they look like indoor shots. This means both you and the camera and the child must be still and steady. The suggestion of a tripod is a good one. Another option is more light.
Does this camera/lens combo deliver sharp photos when you are outdoors in good daylight? If it does than what I explained is the problem. If you never get sharp pictures than you may have faulty equipment.
EB
EOS 1DX and 1D Mk IV and less lenses then before!
