I have a 2 and 5 yr old and have been thru a bunch of cams after leaving a 5D2 I shot with for 3 yrs and started churning cameras. If AF acquisition speed in low light is your primary concern then one of the m4/3 cameras with -4EV AF is a great option. Tracking sucks but single AF is so good you can get a lot of keepers. That is my recommendation currently having A7ii, A7s, GH4, EM1 and GM5 and X100T and having dived back into dslrs for a bit with a d800.
a7s is awesome for kid shooting based on ability to maintain high shutter speeds but AF acquisition speed isn't on par with m4/3. Just today I took some pics of my moving 2 yr old with the FE 35/2.8 (quick to focus) in single shot AFS and when I looked closely they were out of focus and noted that my GH4 would have nailed it.
I remain tempted by the smaller D750 with smaller primes as a stopgap measure until AF performance converges but I don't need more options on what to take each day.