Mathias
While I don't have any children, I find that it all starts with the parents. I deal with the general population on a daily basis and the one thing I have the biggest struggle with is getting my clients to change the way they eat and think about food.
A child's sense of reality which shapes them as they get older stems from people of authority (parents, teachers, clergy, coaches, etc.) who are all adults. The kids are fed junk in school. There are vending machines in the schools. All too often I have friends who are parents who sheepishly tell me all the time that they ate The Golden Arches because it's easier, more convenient and their kids were crying for it.
As for you, it's no different than what I preach to my clients all the time. You need to be pro-active about your diet and if you plan ahead and carry around a small cooler when you are on the go, you will find that it is easy to stick to eating clean. However, if you do have to do the takout thing, I recommend Chipolte's or Moe's. You can get away fairly healthy in there. Also, when in doubt, you can never go wrong with a grilled chicken sandwhich however, regardless of where you go, you will encounter the ridiculously high sodium levels in restaurant and take out food.
All in all, from reading your post, you are doing a great job.
"It ain't about how hard you hit, it's about how hard you can get hit and keep moving forward" - Rocky Balboa
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Now, those of you that know me know that I love to run and and for awhile there I was running quite a bit while training for my marathon. Maybe it was the 8 and 10 mile runs that turned them off hey? 
Sometimes you just gotta!!!! 
