After shooting the Leica M and S, I'm surprised at your choices and what you decided on. However, I understand the need for quick AF and lower light abilities to capture those squirmy, kinetic kiddies ... priceless family memories that will increase in emotional value as they grow up. Oddly, I shoot non-stop kids and families in action professionally, and rarely use anything other than the S2. However, these situations are controlled timings, and I pick the time of day and where. So, it is not the same challenge.
I've flip-flopped between Canon and Nikon for decades of shoot weddings ... (weddings have similar AF and lower light demands to what you are after), and in reality the differences are usually subtile. In the end, my selection was neither Canon or Nikon ... choosing Sony for the Zeiss AF lenses that came closest to the Leica look and feel (closer, but not the same), and that all lenses are in-body stabilized ... including the Sony 50/1.4, Zeiss 85/1.4, and incomparable Zeiss 135/1.8.
Here's a tip for working with slower focusing Canon lenses like the 50/1.2 and 85/1.2 ... get a STE-2 for the hot-shoe. It projects a pretty crisp focusing aid that significantly increases the keeper ratio in lower light AF situations.
I had a chance to shoot with a friend's Canon 5D-MKIII while on a mini vacation just last week. The first thing I took note of was the different sound/feel to the shutter compared to previous 5D models. Better. The files were typical Canon look and feel to my eye (lenses probably) ... which is a subjective evaluation.
Best of luck with your final evaluation. All that matters is that you get the shots and preserve the childhood of your kids :thumbs:
-Marc