Anyone who's ever been at home with a child between the ages of 0-7 knows they pretty much need constant attention. Maybe you can put older ones in front of the TV and get them to a vegetated state while you write code for an hour or two at most.

Doing it occasionally with a sick child is understandable if it's a rare occurrence. I've done this quite often, but even then I'm always playing catch up at night after they go to bed. It wouldn't be sustainable every day.