@ alwaysjerriky - Why would it be overkill? I'd argue that when it comes to photographing kids, it's even more so that you need a wider aperture, fast focusing lens. For one thing, you have less control of the environment. For another, kids tend to move around alot.
@TS - on APSC 50mm will become a short tele of around 85mm, which is wonderful for portraits. However, it also means you have to stand quite a bit away from your daughter to get a full body portrait. Not sure how convenient that will be for you.
50mm in both FF and APSC equivalent terms is neither long nor wide. Some background compression but not too much. It has a wide enough view without much corner distortion.
If on FF, the 35 will be more versatile since it's easier to do environment portraits without having to stand further. People say it's usually only a 2 step backwards for a 50mm to get a 35mm view. In practice with kids though, it's not always an option. And 35 is a bit wide so depending on your composition, there might be some distorted body parts.
As for the lenses, both are very good although the 35 1.4 is getting on in years. It's forever rumored to be replaced soon. I have the 50 1.2 but have only tried the 35 1.4. I think the 35 focuses faster but I find I like the 'look' of the files better with the 50 1.2. Both are equally big and chunky. The 50 is weathersealed, the 35 isn't. Both are built like tanks.
I'm sure other CSers will chime in with the Sigma 35 1.4 soon but I've never considered that one and not because it's a third party lens.
As for me, I started on the 50mm but I'm now using 35mm more as I find it more versatile. When my kids were younger I used the 50mm more though