That'll do it for sure , parents would sometimes do better to simply let the behavior go, and that they are feeding the' frenzy" by the attention the child gets from the behavior.and the child knows this .Actually we all do it sometimes even when we are "Grown" up.
I agree with Margy, she's getting rewarded for crying somehow.
My middle son was obstinate in his younger years and we dealt with it by setting time limits. If he insisted on saying "WHY CAN'T I DO THAT? WHY CAN'T I DO THAT"? etc., ad infinitum, I'd set a limit. You can say that to me 8 more times and then if you want to keep saying it you have to go to your room to say it. I'd say keep going, you can still say it 2 more times. Do this calmly, in kind of a helpful detached way. Like you're counting jumping jacks. Kind of detached, but helpful. He had a 3 minute tantrum limit, and after that if he still wanted to scream he had to go into his room or the garage, it was his choice. I'd set the timer, you have three more minutes to scream. If he'd start to wane I'd look at the timer and say you still have about a minute if you want to keep going. Detached, calm, helpful voice.
It was incredibly affective. I think it was really irritating for him to be encouraged to keep screaming when he was trying to catch his breath.
Best wishes.
Ignore the crying yes it is annoying and I am sure she knows it is , do not feed into it. Let it go ,Focus on the positive side of her behavior , she will stop when she knows it is not getting her attention,.Give her plenty of positive attention, Games ,Reading sports , doing things with her, get her Dad involved in outside activities and Fun.Parks ,Walks .