My 2 year old is out of control it is bad I really need help so plz plz read!! PLz i know its long srry!?

FIRST OF ALL....this is really long but I seriously need help! This isn't another stupid yahoo answer question like am I fat or what color should I dye my hair or whats a good movie and stupid things like that this is a very serious question and i am need of real help from people who are willing to give me the best advice they can possibly give me and I really really need it so please take the time to read this in full and help if you can. If your a parent or a doctor or you know anything about my situation please let me know what I can do............Ok SO....my daughter is REALLY BAD!!! She does not do ANYTHING I tell her when she is doing something bad and I tell her no she just continues to do it I have tried time outs I have tried getting down and talking to her and trying to explain that it was bad and teach her to be good but she just won't. I have even finally resorted to which in turn taught her I think that it is ok to hit and now she hits me and her dad other kids that come over she even hits herself when she gets really mad. She freaks out if I even try to disiplin her she will scream for hours and hit and kick and throw herself around and im at my wits end im a first time mother I have no idea how to deal with this my family doesn't know what to do with her either. When she isn't being bad she is great she can be sweet and funny and she is REALLY smart she already can count to 15 by herself and do her abcs almost all in a row by herself but doesnt quite got a few of the letters down but almost every one. She is great at problem solving and understands things I can't even get a 5 year old to understand. She can talk really well and knows lots and lots of words and she uses sentences to explain what she wants or what she is doing. She knows lots of kids songs by heart like twinkle twinkle little star and many many others and can recite them almost word for word. She knows the differences between colors and is able to point out all the basic colors like red and green and blue and yellow and she loves pink. She is really smart she finds ways to get what she wants like she wanted a popsickle out of the freezer and I told her no she looked mad but quickly went over and got the broom and stuck it in the handle of the freezer and pulled the freezer open and stuck the broom in the freezer and began trying to sc the popsickle out of the freezer. That quickly she figured out a way to get what she wanted all on her own. She knows how to turn the volume up or down on the tv and how to work our dvd player she knows how to turn the dvd player on take a dvd out of its case put it in the dvd player push play skip through the commercials to the actual movie then press play again and she never lets us watch anything we have to put the dvd player up so she cant use it. And even then if she wants to watch tv she will go to the tv and repeatedely turn the tv off on us intill we turn it to a cartoon. She is already potty trained and does that all on her own she knows how to lock and unlock our deadbolt on our door so we cannot leave her alone for one second because she can unclock the door and leave anytime she can go up and down stairs all by herself she can even draw circles already she loves to draw and she is drawing almost perfect circles and understands what she is drawing when she does it and she can almost draw a triangle and a heart she even points them out to us and tells us what it is that she drew. She is a delight when she is in a good mood but as soon as she doesn't get her way she turns into a nightmare and will get really mad and she doesn't care what we do I have tried everything I have looked up internet sites for it and its all confusing to me ive taken her to a doctor and they said she is just acting out because of terrible twos but I know she is different then that. Could it be she is understimulated because she is so smart? I really do not know but she will bite and scream and when I tell her no she just yells and tells me know back or does it anyway i have tried confining her to her room but she will scream for an hour straight and bang on the door and i give in and let her out. She knows what she is doing I can tell she understands that she is getting in trouble and she shouldn't be doing something but she thinks she can do anything she wants she thinks she doesn't have to listen to me how can I enforce the rules and get her to calm down and do what I say. I mean she isn't a demon child she can be really sweet she gives me hugs and kisses and cuddles and she loves us both and I love her alot to she can be a real joy to be around intill we try to disiplin her and then she turns into a completely different child. Sometimes we can tell her to do something and she will do it but it doesn't last long and its only sometimes. Then there is times she will just revert to something else and do that instead and its something she knows is bad like she is testing me to see how much she can get