I think my 6 year old needs therapy

I feel like something is wrong with my 6 year old daughter. At school she is an angel, absolutely perfect. At home she is nasty, tells her brother to do things to get him in trouble, spits, flips out if she’s told no (she we stick to it). Tonight she had a 40 minute tantrum at bedtime because we wouldn’t let her have second piece of her brother birthday cake. 40 minutes!!!!! When I try the calm down strategies with her she just yells at me. When my husband tries, she hits him. Is this normal? Half of the people I talk to say yes, others no. I’m so unhappy. I really don’t like being around her.