First of all, this isn't "normal two year old behavior". My kids never acted like that. The reason I say that is because I don't want you to end up dismissing the behavior as a "phase". If you do, trust me, you'll have it much much worse in a couple of years when she's able to fully communicate with you and also begins to think that she knows everything. What I would do, and have done with my own kids, is find something that she finds sacred. When you do, whether it be a favorite toy or a favorite show she watches on tv, take it away from her when she starts acting up, and let her earn it back. Also, when she starts acting up, just take her into her room without saying anything to her, and tell her calmly that she can come back out with you when she's done crying. You really have to choose battles with her too. If she starts screaming when you are trying to change her diaper, then let her sit in a dirty diaper and tell her when she's ready to let you change her and make her more comfortable, to let you know. As far as kicking and hitting, that behavior is severe for that age and should be unacceptable. Definitely make her apologize, and take her favorite toy away for a while. If that doesn't work, try standing her in a corner, or maybe no tv for an hour. When I was first teaching my kids about proper behavior when we were out, meaning no screaming and what not, I practiced with them at the mall. I'd put them in the stroller and if one started crying, I'd quickly go down a hallway where a bathroom was and stop. I'd tell them "No crying in stores. We're going to stay here until you're done, and when you're done, we'll move again" Believe me, it didn't take more than a few times of finding a hallway to wait their tantrums out before they realized how boring it was to just sit there. I mean, I wasn't getting upset, which is partially why they throw tantrums, to upset their parents and get their way. So, since I was just letting them wail it out in a boring hallway, they quickly learned to "not cry in stores". Even after the mall practices, I would do the same thing in Walmart. I'd stop the cart right away when they'd cry and the crying would immediately stop.
When my kids have days where they're whiny, I have a "whining chair" where they go each time they whine for no good reason. I've also sent them to their rooms until they're done. This way, noone else in the house is suffering from listening to them, and the child who's acting up as isolated herself and will quickly learn that the behavior isn't worth the consequence.