The closest thing I can compare fatherhood with is the vocation of priesthood. You don't stop ministering to your parishioners even when you're eating your meal. Priests pray for the people too and officiate mass for them to link collectively with the Divine.
That's what fathers do at home or otherwise.
It's more like being a police officer who doesn't stop arresting pickpocketers on his or her way home from his shift at the station. It's also more than being a soldier who does not rest from responding to calls of duty even in the middle of a vacation.