I don't think there's any "weird setup", other than having a separate room for work/computer. It's pretty good insulator for all the interruptions. And of course, better coffee.
The additional productivity probably came from the added time per day and reduced fatigue from lower amount of noise (office room vs. open office floor). I don't think there's anything weird about it, I at least found working at the office very tiring since concentration was difficult and required energy.
Mostly teaching them. "When dad works, don't bother him". And since I do come out of the room in any case often enough (coffee/toilet/eat/etc), they saw me enough often. But it's not like single productive period is a long time, rather it's a patches of smaller events during the day.
Of course now that they're bigger, everything is a bit different.
Let me ask this directly. Is your wife watching over the kids while you get productive time?
If so, then that's not a luxury many people (including, you know, many wives) with small children have. Hence the comment that you originally replied to makes sense.
The additional productivity probably came from the added time per day and reduced fatigue from lower amount of noise (office room vs. open office floor). I don't think there's anything weird about it, I at least found working at the office very tiring since concentration was difficult and required energy.