C.H.
I have two daughters, 6 and 2, also but they are further apart in age than yours. I truly think that with girls...it's all about the drama. Admit it, we all have a little Drama Queen in us, (grin). My oldest daughter is 6, almost 7. She's a huge Drama Queen, to this day!! She and my son who's 10 used to scream at each other when they'd fight. You have to be patience and calm, while letting them know that screaming will NOT get them anything they want nor will it be tolerated. When my oldest daughter would scream, I'd put her in her room. I'd tell her that she can scream all she wants in there but I WOULD NOT listen to it. Then when she had finished, I'd go in and ask her to quietly tell me what the problem was. It's a HUGE pain but it will pass once they learn to control their emotions. Hang in there because although age 3 is worse than 2, it does start to get better when the child gets close to 5.
As for how she behaves in school, that is normal too. Kids who have meltdowns at home, tend to be angels at school. Be thankful. I was a preschool teacher for a while. The kids who would lose it at school, well when I'd tell their parents what happened, biting, hitting etc.., the parents were shocked and like, "Not MY child! They never act that way at home." It was like they were implying something was wrong at school. All toddlers and preschoolers have tantrums. It's normal and they can learn to control it. It just drives us crazy ubtil they do, God's little payback for how we treated our parents. LOL!
God bless!
Chris