Adults throwing tantrums
I'm going to swing slightly in the opposite direction with my experiences. Yesterday we had a interdepartmental meeting and something very interesting happened.
My supervisor uses her emotions to intimidate people and it usually works. She regularly throws tantrums, but not the kind where she starts wailing and crying. She sputters and literally starts pulling her hair and you can tell she's beginning her routine. I don't know if she is truly unable to modulate her responses and reactions to those of the people around her or if she's authentically responding. My colleagues are so wary of her responses that ignoring her (the typical response) actually validates her response in her mind. No one says anything to her about it so she continues as she has.
I have occasionally ventured out there to tell her her responses are unprofessional, create tension in our department, and are completely disproportionate to the problem. I have been accused of insubordination and was even told "I'm the boss! You're the employee!" I've since tried to limit my interactions with her, but it's hard cause she's my direct supervisor and we work closely together.
But what was so interesting yesterday was we were at a meeting with IT discussing the execution of our projects. The IT manager was PURE GOLD

. When my boss started her antics she told her in a very stern tone that she will not have her people subjected to her antics and that she would end the meeting immediately. My boss quieted down for about 20 minutes or so before she started up again and the IT manager shut her down. My boss said nothing for the rest of the meeting. It was pure bliss.
Now I think what helped the IT manager is she won't have to deal with her on a daily basis. When/if my coworkers and I directly confront her about her behavior we have to deal with the nuclear fallout. I personally don't deal well with someone sulking or passively trying to punish you for any perceived wrongs you do against them, which is what my boss is famous for. In a work environment, if you don't have a strong director or whoever the head honcho is who actively mitigates conflicts between employees behavior like my boss' poisons the atmosphere and no one (or maybe it's just me) feels like they can say anything against the person who creates the toxin it creates a domino effect of other people starting to erupt because of all the pent-up frustration caused by ONE PERSON.
So like Jennifer said, how to deal with a person who throws tantrums is really dependent upon your relationship to and with that person. In my case, it's not a family member it's my supervisor. I can't deal with them the same way I would my sister or brother or even a friend. Ignoring a family member may work, but that's not necessarily the case in a professional relationship. You shouldn't have to play counselor/therapist with someone who's there to do a job and it's not unreasonable to expect a modicum of professional behavior from an ADULT, i.e. not throw tantrums as a means of controlling your environment because people don't want to deal with it.
OK that was a semi-rant, but I feel you. I have to deal with it on a daily basis and I'm at loss what to do myself.