I swear I saw the same thing happen on that John & Kate plus 8 show.... i don't remember what they did to resolve the problem!
I remember that episode. There kid did it when they would leave her in the kids area at church. She was older though(3 maybe.) I think they told her if she threw up she would have to stay in the same clothes and they would be stinky etc. I think that is what stopped them.
I don't like giving into tantrums or touching the child but sometimes it is necessary for a parent to intervene. Every child is different. Maybe try something a little more AP. Hold her firmly until she calms down. She may just need to feel safe and secure. Is she getting enough cuddle time? Also make sure you totally lavish on the praise when she does something right. "Give me the toy" she gives it to you "Yay! Awesome! Way to go DD." Give her kisses, a high five, whatever motivates her.