R.,
Just remember, your little complex intelligent person is a child, so she is doing what is natural for her, and she is right to do that, to be herself.
Our job as parents, in my opinion, is to know when we are being "triggered" by our children's behavior (we feel embarrassed and just want it to stop, or they are doing something that we were shamed about or our parents squashed, etc), try to feel our own feelings and own them, then respond to our children, realizing what they are doing is just being children, and not really trying to make us feel all of that awful stuff! Then we need to really try to *see* our children and understand what is happening in their world at any given moment and help to translate it for them, to guide, support, and interpret. Our job is also to help them understand how to live successfully in our culture, but I think too often people punish developmentatlly appropriate behavior. Parents almost always mean well, but i think punishing developmentally appropriate behavior comes from not understanding how a child of a certain age thinks, and the true limits of their capabilities. I love the book, how to talk so kids will listen and listen so kids will talk. I also think the baby book by dr sears is a good one as it has a lot of developmental info in it to help parents understand their babies and toddlers better. She is right on target for her age, which is, she is just NOW realizing that she is a "me," separate from you, her mom. so, in some ways, celebrate her "mine" stage, it means she's healthy! I would always try to give information when correcting her, but acknowledge this discovery of hers as positive (even though it comes out as socially embarrassing) and then redirect vs closing her down. I might say, Oh! you are "you," yes! And you have your OWN toys, like this one (have one handy), and this is YOUR toy!" X is playing with that toy, do you want to play with that? OK, x can she have a turn with that when you're finished?" Oh thank you." You are modeling behavior you want, giving her something to work with. i think she will respond to this with more understanding and it will be more productive for you both. She is just beginning the long journey of knowing where she ends and another person starts and whose is what. I think a loving and understanding approach is the best one. Good luck!
PS When she's throwing a fit, she's not trying to be a jerk, she is acting out the way she feels in the only way she knows how *RIGHT NOW*. she is frustrated or overtired or overcome with emotion or trying to say something and can't or etc etc. at her age, she doesn't have a lot of skills yet and that's ok, she's SO little! i would try to understand her outloud and then give her some other options, or just move her to a safe place to have her tantrum and then process it with her - man you were frustrated about x, i can see that. let's see how we can work this out.... or wow, i can see we stayed at the mall too long, you are tired, i'm sorry! we'll leave sooner next time! and if it's not a situation like, woops, i haven't fed her, or she's really tired, or whatever, work it out with her, ok sweetie, next time that happens, you can say this to mommy and i'll help you. i'll pay attention too and see if i can help you sooner. etc. Also (boy i'm on a roll tonight), i would be wary of making bed a punitive place, that might come back in a negative way. you want bed to be a place she wants to go!