I'm doing that right now, one thing I learned after my first child is: do your best to be efficient with some good level of effectiveness and deliver your expected output (which should already be reduced) in less time. E.g. Use the time for errands to think on how to approach a problem for example.
Now on the second one, I'm doing sort of this schedule:
- mornings to lunch is work time, my wife looks after the little one, the older one is at kindergarten
- lunch is not short break, usually from noon to 2pm, time with the wife and with the little one
- 4pm-ish full stop as the older one gets home, I don't accept meetings after this time
- 8pm-ish bed routine, sleep 1hr-2hr or so with them
- wake up, grind some work until hitting a goal
- weekends: I do some prep work for the week, but is 3 hours tops in 2 days
The little one is 1y old now, and this have being going like that for 6m or so, is it healthy? No, you need proper sleep time to be able to give care.
Do I work 8h day? Definitely not, 8h is really rare right now.
I've tried shifting my schedule to start very early, like waking 5-6am but I did not managed to switch.
This does not work on the long term I believe, there were weeks where I fully skipped the night shift and only did the work I could during the day, as I felt that I wasn't able to give care and attention properly being tired.
