I agree with 80% of what you wrote. Temper tantrums really are a just a way in which women try to passive aggressively get men to submit to whatever idiotic demands they make. If you argue back with them, they play victim and accuse you of being the aggressor because they know full well that our liberal, effeminate society will side with her because she happens to be a woman (even though in their hearts people know she's the aggressor).
The victimhood card is a woman's Ace In the Hole which is why women will, in particular, choose public settings to throw temper tantrums because they know that if a man defends himself by arguing back, he will be labelled as the aggressor by our liberal effeminate society. Or if he submits, she wins and loses all respect for him.
I do agree that in that situation, the best option is to address the other people in the room and point out her behavior, however, it would not be wise to take a snarky tone(yet). I would encourage taking a more mature/tempered tone and say something like "Jane is feeling a bit emotional right now, let's give it some time for her to calm down and then we can have a rational discussion about (insert topic)".
I would then proceed to ignore her for a while and socialize with other people in the social circle - making sure that my demeanor is friendly, fun and light-hearted with everyone else so that it will further emphasize that she is the one acting like a fool. Eventually, she'll get frustrated and try to start an argument with someone else and this will annoy everyone else in the group and they will start ganging up on her and putting her in her place.
Usually what will happen next is that after a while, she'll try to start a conversation with you again as a way to open a line of dialog so that she can, once again, throw another temper tantrum to test you a second time. When she tries to talk to you again just ask her loudly and make sure everyone else hears "Are you feeling better now? Have you calmed down and collected your thoughts yet?". At this point there are two possible outcomes:
1. She backs down. You can now take a snarky, sarcastic, condescending tone IN FRONT OF EVERYONE because it's already been established that she's the one acting foolish. This public humiliation is her punishment for daring to challenge you. She's gonna know that you don't put up with nonsense and that you aren't afraid to punish her for bad behavior - the same way a parent punishes a child for bad behavior.
2. She throws another temper tantrum. If this happens, you can also take a snarky, sarcastic, condescending tone IN FRONT OF EVERYONE because now they know that she's the aggressor and that you're just putting her in her place for bad behavior. The other people in the group will have a harder time labelling you as the aggressor because they know you've tried your best to be mature but she's being unreasonable.
Outcome 2 happens slightly more than Outcome 1 - outcome 2 happens about 55% of the time, while outcome 1 happens about 45% of the time.
If outcome 2 happens, you now have to take a more aggressive and active role by not only verbally being sarcastic IN FRONT OF EVERYONE, but behind the scenes you must now start SUBTLY basing her character. This is how we plant seeds of doubt in the minds of her friends. Eventually, she's gonna do something to p1ss off some of her friends (again) or p1ss off another male in the group and this will serve to reinforce that she is the one being unreasonable.
Continue planting seeds of doubt. Continue provoking her to throw even more tantrums - repeat the process until she is isolated from her friends. Eventually, she's gonna stop because a woman is less inclined to throw a tantrum when she knows that no one will side with her.
Will she come around and submit to you? Probably not. But you've made an example out of her and other women in the group know that you won't put up with BS which will deter tantrums from other women.
Is this approach effective? Yes it is. Is this approach childish and petty? Yes it is. But unfortunately this is what our society has come to, and we have to adjust our game to fit this SJW infested world.