Considering updrading from RX100 to NEX-5N or NEX-6

The NEX 5N would be a much more logical purchase for your needs than the twice the price NEX 6.  The 5N could even be further discounted around Black Friday, but its quite unlikely the NEX6 will be reduced at all, since it was very recently released.  The kit lens should work reasonable well, or you can add the Sigma 30mm, which is a great lens for only $200.  The 16mm lens a commenter mentioned, while small, is not a good focal length at all for taking close up photos of children.

Its easy to spend a lot more money and get little or no added benefit in photography.  Analyze your needs and the alternatives before you make a purchasing decision.

Hope this helps.

Joel