Terrible two's or something more?

I don't know about the Aspergers or anything, but I would walk away when my kids threw a tantrum. A tantrum thrower is like a mini terrorist - they want an audience and a reaction. Take both away, and the point of the tantrum is lost. If she follows you, pick her up and put her in a time out spot and walk away. Tell her firmly and calmly "no" and that when she calms down she can come in the kitchen and have a drink with her sister and you. But I hope and pray everything goes well with you... twos and threes are so much fun! Patience and persistence... :)