Upload & Sell: On
You mentioned that your children are involved in sports/action, at least some of which will be low light work. If you intend to try to capture images of both of your children in those activities, I'd suggest getting the body with the best AF that you can afford. To me, that means cameras with the multi-cam 3500 module, like the d800.
If I were in your shoes, with a $2500 budget for the body, I'd get either a refurbished d800, a d3 or a d700. If you could stretch a bit to about $3500, a d3s would be the ticket, IMO. I own the d3s and a refurb d800, along with the d700/d300, all of which are 51pt cam 3500 AF cameras. I would rank their AF performance as I've listed them. I also own a d7000, which has the 39pt multi-cam 4800 AF module, the predecessor to the AF module in the d600. IMO, the d7k is at the bottom of the list for AF performance.
Although I think that a d3 would outperform the d800, perhaps significantly so at times, the d800 still has some advantages, primarily pixel density, so I'd put them almost equal in value.
Here's a link to an article which tested the AF tracking performance of the d4, d800 and d600, which also has some interesting comments by readers at the bottom of the page. http://www.naturalexposures.com/corkboard/testing-the-nikon-d4-d800-d600-in-predictive-auto-focus/
Just some food for thought.