I'm a dad with a 2 year old as well.
I generally roll two things. Either a full size backpack with tons of stuff (heavy; and I hike with this and travel/go out with this). Or a shoulder bag (messenger style) that fits a lot less. I actually really enjoy the smaller bag, because it forces me to take less stuff. I generally pack at least three cameras with me! So forcing me to go down to one or two cameras and one or two lenses and one flash and a mini-tripod, one or two filters tops, and some batteries, works great for me. I use a Lowepro Event Messenger 150 for my common days. I can manage two, or three cameras depending on the configuration. Generally though one big camera and one fairly large lens (medium zoom tops). A filter, some batteries and some other stuff can go in the front zipper.
What I generally pack:
One full size gripped dSLR with with a 40mm pancake lens and one other large zoom or prime next to it (why use a body cap when you can use a lens!).
One speedlite and a mini-tripod (ultrapod II) lays over those.
Spare batteries in the front. Wireless shutter release in the front. One filter (either a CPL or a 3 stop ND; depends on what I think I need).
I can usually throw my EOS-M with 22mm pancake lens in there too, it's so small.
Back flap has room for a small baggie and other thin or paper type goods where I generally take a mosquito net and other stuff.
I throw my Joby strap in there, so when I know it's time to shoot, I use the Joby so I can drop the camera and grab the kid if needed.
That's the Event Messenger 150. It was like $20. Mica color (whatever that is? It's like gray/green?). Holds up great. I take it every where.
I thought about getting the next size up, but it was ultimately large enough to tempt me to take a 3rd & 4th lens, or 3rd camera body, more flashes, etc. I'm a pack rat for gear. But I love having duplicates and I usually always have a prime and zoom, or several primes. Depends on what I'm doing.
Current pack (just put it all in, fits nice):
Event Messenger 150 Bag
In main chamber:
Canon 1D Mark II with EF 40mm F2.8 STM pancake lens attached (free lens instead of a cap!).
Canon 200 F2.8L prime (built in lens hood, MK I) sitting up next to it. Fills bottom of bag.
Wedged in the corner is an Ultrapod II mini-tripod with ballhead (it's that small and can hold quite a bit).
Laying over top is a Yongnuo 560 III speedlite, I store it in an elbow shape with the barrel down, to make more room.
An EOS-M with 22mm F2 STM pancake lays on top of that (again, free lens instead of a cap, and the camera is so small!).
Front zipper chamber:
1D Mark II battery #2
EOS-M battery #2
Yongnuo RF603c transceiver (for off camera flash, it's so small).
Marumi Super DHG CPL (77mm) with a few step down rings ** (72mm, 52mm, 43mm I think?).
Wireless shutter remote + dongle (very small).
Extra AA batteries (x4) & AAA batteries (x2).
Extra CF & SD cards.
Back slide in chamber:
Mosquito net for face (goes over a hat).
Step down rings mentioned before **.
Still room to slide a 7" tablet back in there.
It may sound like a lot, but trust me, it fits in a small space if you pack right!