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even though I have posted earlier, I will give a little more perspective as a father of 2 young children (5 years and 7 months) whose childhood is very well documented.
Wtih my first baby, I purchased the original 5d, and used it with a tamron 28-75 2.8, and a 50 1.4, and a 70-200 2.8 IS. it all worked very admirably. I liked the close focusing of the tamron, and over all happy with low light shooting. I had a separate video camera. then I upgraded to 5d2. I loved the video, but it was not as easy and simple to use because of focus tracking. fine before they started moving around, but harder as they get older. accumulated a bunch of lenses, and looking back, my most common lenses became my primes. (50, and 85). I had a 40D alongside for a while which my wife enjoyed using b/c of smaller body. she took many great pictures of the kid.
Now, I also have the nex 5N. my wife loves it for video. the autofocus can be a little frustrating if you are used to dslr. this is esp true if you are shooting a fast prime. I do use it myself also on outings, with good light, as a light camera instead of my dslr, and also to social outings. it does great, however I love my 5d3.
second time around, I am also shooting more wide (35, 24 primes) which has a nicer documentary feel.
However, looking back at my humble 5d images, I still find them quite good. make sure whatever you get, your wife likes using.
as for flash, I have done them both ways, just using window light, and using strobes. for new born when they are asleep, strobes are not an issue. with away babies, I still use them, but also use a lot of windows light, which works pretty well with f 2.8, or even f4.
for example, these were taken just over the last couple of days with just window light.
another at 2.8
anyways, many ways to skin a cat, and the all work. the modern cameras, full frame as well as cropped dslr's and the nex and micro 4/3rds are so good, that you can make any of them work. for that matter your 1ds is excellent, except for size and lack of video, esp if you put a couple of primes (I recommend sigma 35 1.4, and canon 85 1.8 if budget allows)
sorry for the long winded write up, just that I have been trough it. as i said in original post, I think 6D would do just fine, though I do recommend a relatively small fast prime.