You need at least 2 key things for low light action photos:
1. A larger sensor with good low light performance (low noise at high ISO)
2. A fast lens with large aperture, at least f/2.8 or larger
Other things that will be nice to have include a good AF system and fast fps.
The NEX is not really a low light action camera. It has an APS-C size sensor but the system does not have fast tele. You will need to use the D-SLR line of fast tele, these lenses are pricy and hefty, pretty much beat the purpose of having a cheaper smaller camera body.
But whether the NEX is adequate for your need will depend on what you mean by kid and low light photos. Many cameras including the NEX can make very nice low light scenic stills with a tripod and slow shutter speed. NEX will also do a decent job in light painting shots. The NEX can take very good outdoor actions with good lighting. If your definition of low light action is something equivalent to a well lit basketball stadium, then NEX can be adequate. But if you mean taking night action photos in a poorly lit neighborhood park, then NEX will not be a good choice. In those poor lighting conditions, you will need a fast f/2.8 or larger tele lens and at least ISO 3200.
As pointed out above, flash photography is also not a strength of the NEX, since it does not have a powerful external hot shoe mount flash available.
So if you need to take good quality photos in challenging lighting conditions, then you will be better off staying with the D-SLR. But if portability is more important, then NEX is something in between PS and D-SLR.
I HAVE READ MANY POSITIVES REVIEWS ABOUT THIS CAMERA,WOULD THIS CAMERA BE GOOD FOR TAKING PICS OF MOVING CHILDREN,LOW LIGHTING SCENES,ANYONE WITH EXPERIENCE WITH THIS UNIT WOULD BE GREAT,THANKS....PGANT