Hi K.,
I am a mom of three and I was also a preschool teacher for thirteen years. My advice on the "drop off drama" is to make the drop off short and sweet. Decide how many hugs and kisses, stick to it and go. DO NOT react to her screaming, it is just a show, for you. It is her way of letting you know that you will be missed. If, however, her behavior at the end of the day is similar to drop off, I would try to figure out what is going on further.
As for the hitting, the most important thing you can do is model the behavior you want her to display, which means no hitting or spanking. Tell her that there is no hurting allowed. Explain that this means NO hitting, kicking, biting, pinching etc. It is YOUR job, as a mommy (and daddy) to teach your children to be "safe and kind". I have been teaching that to my children for 12 years. Of course the siblings fight, but they know there will be a consequence for hurting eachother. My reason is always that "it is my job as a mommy to make sure you are safe and kind." I am sure that the preschool is dealing with the hitting at the moment, so there is no reason for more punishment at home, but you can express your dissappointment for her behavior and again remind her "no hurting".
Sorry this is so long. Please know that this approach does work. My children rarely resort to hitting, I know of so many other families that don't use this "philosophy" and their kids beat eachother up at every confrontation.
Hope this helps!
Jenny