Well, maybe not $5 a minute, but I would have thought that they would have a policy in place for charging for late pick ups as well as staff training in handling touchy problems. And I would be surprised if late pick ups were not a common problem. You might have gotten the tongue lashing for about 50 other people she handled well over a period of time. And of course, no, she got nowhere by being so nasty. I would have offered a cash apology right up until the point she started venting on me, and then I would figure she made her point and left it at that. I like you would most likely not have taken my child back for fear that she would have been angry all week and maybe taken it out on my child. Human nature prevails and it isn't always pretty.
I admire you for not letting it ruin your cruise. That's the kind of thing that could keep me torn up for the rest of the cruise. But in this case, unless she was just having a bad moment, she is ruining her own health, life and peace by being so harsh on the people she comes in contact with and is probably no longer employed on a ship. She is punishing herself with her anger. I wouldn't have pushed the event any further because I couldn't foresee a good outcome for my child since I would definitely not have taken him back, but I might have written a note about it including her name on my cruise evalution card.