The 7D is good up to ISO 3200 with a little NR in post. I sold an image recently at that high ISO with no flash. It all depends on the ambient light.
Sure the 6D can focus in the dark, sure it performs better at high ISO. But let me ask you, are you taking pics of your kids in the dark? Prob not right? You prob will be down the park or in the back yard etc.
While it less than ideal the built in flash works pretty well in a pinch when you need a little fill. Also it doubles up as a master wireless flash transmitter. Now that has been extremely useful to me. It works really well indoors and outdoors is pretty good. A cheap way to get in to off camera flash.
I use a 7D, 17-55 and 430ex2 combo. Altogether that's about $2k. It's a very versatile setup. Money saved - buy a couple of fast primes like the Sigma 35 1.4 and a 85 1.8. (That gives you like a 50 and 135 combo right there on crop).
Alternatively you'd need a 6D, 24-105, and possibly 2x 600ex rt or one plus a trigger $3k. I personally think that's overkill. I've shot an entire wedding with my 7D bundle. No issues at all.
Btw 6D does have AMFA capability. Someone mentioned it didn't.