The question is sparked in part by the "America's favorite dads in space" narrative which accompanies the recent Demo-2 mission, involving astronauts Rob Behnken and Douglas Hurley, as well as their wives and children to some extent.
Based on the assumption that something of noteworthy character happens to the family members on earth (newborn child, accident, virus infection), what is the notification policy/procedure? Will the astronauts be informed immediately, or only once the mission is completed?
Google hits mostly converge to the reversed situation, i.e. something happening to the astronauts themselves.
I am looking for general answers, not just the recent Demo-2 mission.