Tainted, are you me by any chance?! 
Seriously though, my mother doesn't so much tantrum as turn on the waterworks but it's the same thing - emotional blackmail, pure and simple. The ONLY way to deal with it in my opinion is to refuse to give in to it.
However this is MUCH easier said than done, not least because it's takes years and years before you realise what's going on. I've lost count of the number of times my father or my siblings have tried to get me to fall in with my mother's wishes by saying, "It'll upset Mum if you don't," or, "It'll make Mum happy."
I have only recently realised that actually, I'm allowed to be happy too and do what I want; if what I want conflicts with what Mum wants then maybe she'll just have to be disappointed. That's life. Her feelings are not more important than mine.
I've recently refused to back down over something and it felt so empowering I can't describe it. It was relatively trivial too but was something I just really didn't want to do but I got the emotional blackmail from her, my father and my sister.
As for dealing with it there's a great episode of 30 Rock where Jack (Alec Baldwin) gives Jenna advice on how to deal with the stages of a tantruming mother - although it's a comedy show, it's great advice!
"Say no." If you don't want to do something then say so and stick to it.
"Talk low". When she starts crying, shouting etc, stay calm and lower your voice.
"Let her go." When she flounces off / slams the phone down then don't go after her of ring her back. She flounced off, not you!
Say no; talk low; let her go!