It's not hand-shake. The tell-tale sign of handshake is that the entire image suffers from the same distortion.
In the first image, the hand and the outer eyelashes of the subject's left eye are in tack-sharp focus. It's also fairly wide (f/5) and close up, so anything behind that plane will loose focus, hence the far eye being really out of focus.
In the second, the hand again is the sharp focus but no parts of the eye share the same plane.
This close in, in order to get both eyes in focus you'd have to have an F stop of 11 or so (or likely a bit higher) and focus on the left eye of the subject. That narrow an aperture would still get the hand in focus as well as the other eye.
In the second image, F8 would probably suffice.
In both images, the focus and DOF make the subject the hand, not the child. In terms of color, the reds are a big boosted.
The blown out parts (window behind, I think) are large enough you can mostly ignore them but I did find them slightly distracting.
They're cute pictures though. I'd certainly call them keepers for the memory book.