On the days I work from home, we have a pretty good system worked out. I'm usually a floor away from my kids, all baby monitors are shut off, and they usually head outside for part of the time. I have run into those moments though - when you're home and you can hear the kids acting out, and the nanny having to deal out some form of discipline. (Or not.)
My usual stance is, "I'm not here." To be true to my work, and in my mind, honour the situation. I have to treat my at-home desk the same as my at-work desk. When I'm in the office, I can't hear what's happening with the kids, or how the nanny is handling a situation. The home office needs to be the same.
...I fell off that wagon today.
I could hear K spinning into a full-blown tantrum/fit and the baby screaming as lunch time approached. Dear A was doing her best, but there are days when life comes together into the hurricane and there's nothing you can do. So, I stepped in. I calmed K down and reminded him of the rules around our house. I honestly wasn't doing it to interfere. I wanted to help. But, afterwards, as I returned to my desk I wondered if I'd overstepped. I wondered if by stepping in I'd made it worse for Dear A in the long run.
I don't know the answer. I mean, I suppose, the situation is the same for all parents who have childcare, whether its mid-day or end of day, parents and caregivers each live the consequences of the others "parenting" choices.
It takes a village, right?