You could be describing my nearly 3 year old DD.
And I must admit, it's the most gut-wrenching feeling, as unreasonable as that may sound! Just yesterday we went out with my friend and in the middle of a shop, she stropped and yelled for Daddy. I know this is going to sound so unhinged , but it really hurts me when she says it, and oh does she say it, yell it and scream it ALOT.
I've thought about it alot, and wondered whether it's because our parenting styles are quite different and she prefers his. Not only because he lets her get away with more stuff, but because he is very calm and patient with her and tends to play alot more than I do - because when im at home I tend to 'get on' with things (and mumsnet) instead of giving her as much attention as he does. This makes her whiny and really quite difficult to deal with, and I get shouty which makes her cry for daddy even more 
Could that be your problem too?
Today I tried it his way, concentrated less on the housework (and when I did I got her involved), and got down on the floor and played with her more. I also didn't MN (well, not as much then!). It was very telling when I checked my phone for a message and she said 'nooo mummy! Not phone AGAIN!' I must say her behaviour was so much better as a result. I did get the occasional whinge and one medium sized strop (over wanting 'meat' instead of chicken for dinner, after eating half of her chicken dinner
) but I was calm and a brief visit to the Calm Step helped her calm down and get over it pretty quickly.
And she didn't ask for Daddy once 


Just my experiences - hope it helps. Do post back, I know how bad it can make you feel but it's probably alot more common than we think!