Retouching children's photos to this degree is really appalling in my opinion.

.. Any way, to each his/her own..
What I notice here is an
obvious skin smoothing:
look into gaussian blurring, filter->median, and using denoising programs such as Neat Image to create this effect.. There are many, many ways to accomplish this.
Whitening of eyes:
Use a low opacity brush to paint in the white.. The more white, the more fake..
Fake eyelashes probably:
Either used a brush or copy pasted from a women photo..
Really bad editting of the iris of the eyes:
Generally its more realistic and striking to use brush strokes from the middle of the eye to the outer portion of the colored portion. Add yellow to brown eyes, cyan to blue eyes..
redefine the lip shape:
Use paths to define new lips..