Do not by any means ignore your child, you are correct in doing this...she is asking you for something...her emotional or psychological needs are not being met and she is in distress! This is the time to build trust with her, not abandon her and teach her that her emotions are worthless and something others will ignore!
Would you want her to be a teenage girl who thinks that her emotions are not something anyone is interested in? Do you want her to display emotions as a teen in appropriate way? The toddler years and teen years are very closely related. I have a 19 yo, 13 yo, 4yo and a new baby on the way! You will run into these issues again in her life...deal with it correctly now!
Granted, her approach (tantrums, hitting, etc...) is not acceptable...but that is b/c she is two and needs to be guided though this stage of her development. And don't think of this in terms of controlling her behavior...she needs to learn how to trust herself to control her own behvior! In order to do this she needs love, support, role models, and specific ways of dealing. This is your job, momma :)And the work you do now teaching her and helping her will become a life-long skill that she will be able to rely on again, and again.
I have EIGHT words of advice for you:
Dr. Harvey Karp's Happiest Toddler on the Block.
I am not a big believer in "methods" for dealing with parenting...but his philosophy of dealing with toddlers WORKS...i promise! I worked in a daycare and used it...magic. Now, as a doula and childbirth educator, i work with parents and have first hand experience with what works. Also, as a parent! My DD (now 4) was 2.5 and out of control. One week of Karp's methods and i was sold! She turned into a different child and was so much more happy, confident and in control of herself!
I couldn't begin to write up his philosophy on here, but i think that most local libraries have a copy of his DVD and or book (although the DVD is fast a easy!)You don't want the one about Happiest Baby, that is for newborns. To quote Dr Seuss--Try it! Try it! You will see!