To pile a bit on the parent's take, I think it's just hell if none can set boundaries.

During the stay home period it meant for us that everyday we scheduled who does 100% work at what time, and who takes care of the rest in the meantime (might mean light work while looking after things)

That meant switching back and forth the roles about once or twice everyday, including when the other needs to cook or go to groceries.

In this respect, I think there is just no way to have both parents 100% working at home with a kid needing attention, and trying to reach that will only make everyone miserable.