Best DSLR + lens combo for low light, indoor kid shots

Although not extensively in your particular situation I have used the d5100 in low light for photography in industrial warehouses and at night races on dirt car tracks where i felt it performed quite nicely - not as well as my new D600 - but there is a $1500 price difference.

It was waaayy better than the D3000 I had used previously when it came to ISO noise and low light focus, and significantly faster than my Canon SX50 P&S.

The best thing to do is narrow your choices to a few options and try to find a local dealer where you can test drive them for at least a few minutes.

The addition of good low F prime lenses will help any camera compared to reviews done with the included kit lens.

Below are two pics for comparison that are as close to the same as I had available.  One is from the nikon D3000 with Sigma 10-20mm lens and the other is with the nikon D5100 and Nikon 18-200mm lens.  Neither lenses are great low-light primes like the 1.8G models so this is kind of a worst case scenario comparison. You will see that even at a much higher ISO the D5100 has significantly cleaner images.

D3000 F4.2  ISO-11000  1/30 Shutter

D5100 F5.6 ISO-3200  1/25 Shutter

Those big warehouse lights might look bright but believe me it is pretty dim for any kind of picture taking.