Let me throw in an idea from left field - how about selling your current gear and getting ... an Olympus OM-D E-M5 and two or three lenses?
Now, I know this is a Canon forum but before anyone says I'm trolling, hear me out.
Firstly, I've used Canon DSLRs for the last 10 years and I currently have a 7D and a collection of lenses. I think Canon make great cameras, but I'm trying to focus on they type of photography the OP wants to do and his budget.
Now, from what I've read (and the little time I've spent playing with a friend's OM-D), here's what you'd get with the OM-D
- much smaller and lighter - likely to be a real advantage if you're out of the house and already weighed down carrying all the things necessary for looking after a baby
- probably a bit cheaper, taking into account lens prices
- good build quality with weather sealing - don't think you'd be losing anything there
- an AF system which seems to be pretty good except for tracking fast moving subjects - which sounds like the way the 6D's AF system (and the 60D's too really) is often described - I suspect quite good enough at least until the child is old enough to be running around playing sports
- IQ which may be a lot closer to that of a 7D - and perhaps even a 6D/5DIII(?) - than many of us who are invested in the Canon system would like to admit!
An OM-D plus Panasonic 25 1.4 and Olympus 45 1.8 (remember the OM-D has a 2x multiplier for 35mm equivalent field of view so that's a 50 and 90 in 35mm FOV terms) would be well within the OP's budget without counting the money he'd get selling his 17-55. The Olympus 75 1.8 and Panasonic 12-35 2.8 are other options to consider. Plus the Olympus 40-150 4.0-5.6 is fairly cheap and gets good reviews (and compare it with the price of a Canon 70-300 4.0-5.6!). And the OM-D has in-camera lens stabilisation so IS isn't an issue.
Do a Google search for OM-D v 5DIII comparisons - I expect you'll find it an interesting read, if nothing else. To give an example, have a look at: http://lindsaydobsonphotography.com/blog/olympus-omd-vs-canon-5d-mkiii-nature-photography/
I don't know anything about that photographer beyond what is on her website, but it gives you an idea of the sort of things a Google search can turn up.
I've been considering selling my Canon gear and making the switch to an OM-D because of the lighter size/weight (I'm feeling a bit sick of lugging around a backpack full of heavy camera gear, especially when I'm hiking), but I like doing some action photography so I'll stick with the 7D for now. The size/weight of the OM-D is very appealing though, given the IQ is still pretty good.
For what it's worth, if the OP wants to stick with Canon, I agree with the others who've said the choice is between getting a 7D (and keeping the 17-55), or selling the 17-55 and getting a 6D. In my opinion, the price point of the 7D, plus its ergonomics and build quality, makes it a more appealing package than a Rebel or 60D (although I do know very happy 60D owners). As for the 6D, I haven't played with one so I only know what I read, but it sounds to me like the only real advantage it would have over an OM-D is IQ but that advantage may be smaller than you first expect, in which case the question is whether size/weight/price of the OM-D is enough to compensate. Perhaps a critical factor here is how often the OP will shoot in dim light? It seems the IQ advantage of a 6D (and to a lesser extent a 7D) over an OM-D will be increasingly apparent as the light gets dimmer.