You've gotta do what works for you and one of the big things is communication. I was a bit of a jerk in the early goings (only have one kid) by some standards. Our kid happened to be an unpredictable and not great sleeper so I ran either early in the morning or fairly late at night. I did help out with everything around the house and with our kid, but it can be hard to understand just how mentally and physically fatigued your wife can get.
However, I'm a much nicer person when I get the exercise, and my wife knows that and so she is okay with my running. Kid's older and now sleeps better so I do almost all runs at 5:30, with the occasional run during his nap time on the weekend, but I like to use that time to be with my wife alone.
All told, for me it's not bad. I'm not a morning person by nature but you can adapt. I run in the 35-45 range with the variation a dependence on if my kid wakes early (I'll go in to comfort him so wife can get more sleep).
For the poster who said not waking the family, that's big. In general something else would wake my wife anyway if she's awakened by me heading out. Same goes for my kid, though he does have bat hearing for things like the door lock.
Lastly, racing: I don't do this much. Bringing your wife and kid to the occasional race works for me (if the timing is right), but mostly I skimp. Lots of races is too pricey for our young family anyway.