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You haven't provided a reason for making the upgrade, and honestly the upgrade path is not so simple. Permit me to relate my experience.
I went from a D200 to a D300 shortly after the D300 came out, and while I felt the D300 handled a little better and can offer a usable ISO 1600 (where ISO 800 was pushing it on the D200), I still prefer the colors out from the D200. If I were considering this today, I would not upgrade a trusted D200 to a D300/D300s.
That said, when I started wondering if I should "upgrade" my D300 to a D7000, I quickly realized that I would not be happy with the feel, handling, or AF capabilities of the D7000. Plus, the increase in resolution from a D300 or even a D200 is marginal at best (10/12 mps vs. 16 for the D7000). The D7000's AF may have trouble keeping up with your 4-year olds, especially if you are using AF/AF-D lenses rather than AF-S.
I don't know if the D7100 has a stronger AF motor to drive the older AF lenses than the D7000 did, but at least it offers a substantial increase in resolution and--IMO, even more importantly--dynamic range over the D200/D300 class cameras. Still not sure I'd pull the trigger, but if I were in your shoes I'd give the D7100 a good hard look.
PS To reiterate the correction above, the D7000 and D7100 do have AF motors to drive older AF and AF-D lenses that don't have built-in motors.