SK66 has pretty much nailed it.
As someone in the OP's position (SB600/D90/Prime lens, but with the addition of 3 years down the line on the child front) I can say for certain that the prime is not going to help. Here's why...
1) The D90 kit lens (18-105VR) is around f/4 at 35-50mm. Going to f/1.8 is basically a little over a stop. The relatively good higher-iso performance of the D90 (coupled with our old friend Auto-ISO) makes that a moot point - you still won't have enough light with faster glass.
2) Zoom lens = less framing time. With a toddler on the loose framing and timing will become everything... your subject will not wait while you futz about.
3) You realistically need f/5,6 to get a good facial DOF from anything except them looking directly into the camera. So again the f/1.8 is a moot point at the kind of close-up distances which would make for good indoor shots.
Simply put, you need more light. The SB600 is a vastly underrated flash and using it off-camera makes it the ideal partner for the D90. Also have a read of strobist blog for alternatives (like a combo of PW's and SB-24's or the Vivitars).
Use the leftover money to get a few sets of decent ni-mh cells (like eneloops or energizer accu's) and a decent conditioning / trickle charger like a BL700 - which you're going to need those anyway for the kids toys!
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