Earlier quoted context omitted.
Do you, or will you, allow your children to participate in extracurricular activities? Or is eating every dinner together less of an absolute priority as you claim? Your comment makes it sound like you may have some. I ask because most of the dinners I missed growing up were due to sports.
How late are the extracurricular activities? I'm not American, but at home we would just eat all together after, e.g. around 9 p.m. and if they were later in the evening, we would just eat a bit earlier, like 7.
I think many Americans would look at you like you were nuts if you suggested regularly eating dinner around 9pm. I'd say 5-7pm is the most common here. Often when trips to Europe come up, the discussion is about how you can't get dinner at 5pm because the restaurants aren't open. Although my last few trips to Europe I noticed there are more restaurant choices in touristy areas that open early just to get the American's business. I've also noticed it's better to wait and eat when the locals do. Some of the worst Italian food I've ever had was in Milan at a touristy restaurant, and some of the best was in the same town at a place that a local recommended outside of the tourist areas.