I like the original shot, the one some people think looks too cool. That's the type of rendering Kodak's Ektachrome slide film was famous for. Fuji Velvia was a clownish color super-saturated slide film that was an eye-candy favorite for a few years.
I tried to touch on it above, but let me explain more about what I meant in my first post. First-BABY skin color CHANGES ALL THE TIME, depending on the baby's surroundings. In keeping with that, the baby appears posed outdoors on a chaise lounge, with a thick, pale blue quilt over it, in a Fourth of July outfit. The lighting quality and direction LOOKS LIKE "open shade", which tends to look cooler than say, sun light, where the direct rays of the sun are the source of lighting. This looks like open skylight, summer time. It's going to naturally look ever-so-slightly cool.
We're talking only a few hundred degrees Kelvin difference between an un-coated flashtube, and a UV coated flashtube. We're talking the difference between a BRAND-NEW, non-yellowed umbrella fabric, and a 5 year-old, yellowed umbrella. We're talking the difference between what a baby's skin REALLY looks like when the child is cool, and in the shade, versus some rosy, idealized image of what a hypothetical baby might look like. We are talking about the difference between a Nikkor lens and its Nikkor-family's coolish color rendering (your original upload) and a Sigma lens and its yellow-glass, warm-tone color rendering (the first edit offered).
There is no one, single "correct" color rendering or white balance for every single photo. In your original, it has a look that I grew up with, and know well, and as primarily a Nikon shooter, I prefer the cooler look and the realism of the original skin coloration as I know baby skin to look like in many conditions. On the edit, the reds in her shirt are really popping, and I know that KmH likes to add vibrance and saturation to most images, and I think the reds look clownishly red, and the skin looks wayyyy too ruddy, and the edit looks highly doctored on the skin. The baby's skin does not look "real" to me. I also know that "most people" like too much red, and too much magenta, in their skin tones.
You say you like a slightly cooler look. So do I--most of the time,but it varies. Not every shot is "the same". There is no one,single correct white balance, no one, single way to do color. In open shade, or electronic flash rendering of it, I prefer a COOLER look. I prefer my reds to be more-muted, and less obnoxious. I think the original rendering is a fairly accurate and real look at the way an actual baby tends to look in areas lighted by open shade/skylight/white umbrellas. There's plenty of room for color differences, based on the picture, subject,conditions,etc..