A.V.
Good morning K..
At some point, she has learned that it is effective. Not saying that you think it's ok, but on some level it has worked to get attention.
Be sure that she gets enough attention at other times. Then when this pops up, here are some things you might try.
1)Pick her up & restrain her, hold her tight, tuck her in, sit on the couch, until she settles down. I only had to do this once with my daughter, but I don't think it was to the point you have going on. If in public, remove her as quickly as you can. (this is not to say that having gotten all 4 of you into a store, and leaving immediately will make any of you happy, but you unfortunately do have to content with bystanders disapproval. It's not their looks you care about but one call to CSD will change your situation drastically. They will remove the child, & ask questions later.)
2)You may want to do something that gets her attention & distracts her. Flick her in the cheek with your middle finger. (This is used to stop a biter when nursing) It's sharp & sudden. Or you can try throwing a glass of water in her face, (1/4 -1/2 cup).
3) A trick I heard from a dentist, when a child would not stop screaming: (she was older) was to tell the child to scream as loud as she could & "that's not loud enough, scream louder". In that case it was a power struggle. She was in control, or so she thought. Oh course she quit.
4) One last thought. When at home.... have a scream fest. If she screams, invite your other kids to scream too, And of course you join the fun. Pretty soon every body will be laughing.... She still doesn't get her way, but you have lightened your load for the day.
Hang in their Mama. You've got a little "fighter." that doesn't make her bad, it just makes it more important to get the training in early. She will be a leader. Compliant children may be easier to raise, but these children have a stronger capacity to change their world.