I would have tried to bring the focus back to the welfare of the child. Fighting and abuse in front of the child is not IMO best thing for the kid.
If the "pickup" or "drop off" of a child has the potential to escalate to that degree, may I suggest that it be done in a place where that will not happen such as the police station.
If the "pickup" or "drop off" of a child has the potential to escalate to that degree, may I suggest that it be done in a place where that will not happen such as the police station.