My daughter is in her terrible twos and I need some help!?

My daughter is gorgeous, she's sweet, she's sensitive, she's empathetic, she's very smart for her age (already can recognize over 15 letters of the alphabet). She has my husband (her dad) who adores her, two older brothers who are 7 and 9 and they love her a lot! She has a loving home, loving family. Here's the thing; she's a BRAT! When she doesn't get her way she'll look at you and scream this piercing horrible scream and keep doing it! She'll throw herself backward or on the ground. She hits, spits, scratches and very seldom she'll bite. I've tried yelling, I've tried smacking her fingers, her , I've tapped her mouth. I've even walked away and ignored her. That's what I do when she screams. MOST of the time she's an angel, sweet and loving, ready to help or lend a hug and kiss. But sometimes I have a very hard time. I don't have her in daycare (although I do have two daycare kids who are here during the week) because I don't want her to act like this for anyone else. We've had a LOT of problems with daycares, BAD problems, scary problems and I'm afraid someone is going to get frustrated with her and hit her or punish her badly or hate her and ignore her all day. What can I do that I haven't already done? Any moms and dads or caregivers who have some advice?