I've never used a 7D and don't have children to photograph running around; but I do have a 6D and a 5DIII, plus a cat and a kitten which are faster than any child.... While it's true that the autofocus on the 5DIII is better for photographing moving things than the 6D, I'm inclined to think that the difference is exaggerated and that the 6D is better than its reputation. How often do you like to photograph your children while they're moving around fast? If a lot, a 5DIII would probably make more sense, but otherwise I'm not so sure. Borrow your friend's 5DII if you can - if that's good enough for you, the 6D will certainly be: it focuses better than the 5DII. (Better yet, borrow or rent a 6D so you can see for yourself.)
For things that don't move, I've often used my 6D in very low light and the difference in success rate focusing with outer points vs the 5DIII is trivial. Of course, in terms of focusing accurately when using a fast lens wide open it's better to have more focus points to avoid focus/recompose issues, but I've had no problem using the focus points that the 6D has, while the 6D's center point focuses in even less light than the 5DIII.
And while on the subject of low light, if you often find yourself wanting to brighten dark areas of photos by a significant amount, it's probably worth pointing out that files created by the 6D lend themselves to this better than the 5DIII's - considerably less noise/banding.