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The video will be nice for sure. However,
I would look at picking up an SB700 flash and an 85mm f1.4 lens, if, of course, you don't have one. Probably a 16-35 f4 for some wide family portrait stuff.
You'll love it.
Back t the video, I'd keep using the handycam. I know you probably want to get an all in one unit, and that's a valid point. But the video on SLR's is for more serious users. If you want to do the normal family holidays, the handycam is actually much better suited.
TIP. Limit panning and zooming while recording. Download it to the PC/Mac immediately and do you're editing. Otherwise, it'll sit there and you'll never get around to it.
You sound like a very proud dad. I'm sure you're getting some nice shots.