I'm only so vehement about this issue because it IS so important (to you and to your future relationship with your daughter), so please hear me out!
I hear, 'we have tried ___(this)___' and 'we have tried___(that)__'.
It's time to stop 'trying' and DO something. You are the parents, and you have the right -- NO -- the absolute obligation to be IN CHARGE of this child. She is your 'charge', and that's what this means. Quit trying to appease her, and parent her. I don't mean to be harsh, but if you watch a couple shows of Nanny 911 or Super Nanny, you will see that discipline is what every child needs, and I don't mean spanking (although I spanked my own more than I care to admit. That's how I was parented and it worked in most cases with our 4 now-adult children, but if I had it to do over, I'd do it much less). Disciplining should be more like training a dog than a battle of wills, and I mean no disrespect here, either. It's just a fact that you don't 'teach' a dog by beating or smacking it. You train him/her by being in control -- first of yourself and then of the dog. Reward good behavior, and punish bad behavior (and the 'punishing' can be as simple as ignoring them or making them spend some time away from you -- like in 'time-out').
It's mostly a matter of you YOURSELF believing that you are in control. This strong-willed toddler will wreak havoc on your home if you as parents don't stop it ASAP. And you can.
Don't say anything to her unless you need to (like telling her 'not to throw it'. Nix on that).
Try telling her what TO do instead of what NOT to do (and reward compliance).
Don't say anything to her unless you mean it.
When you DO say anything, enforce it.
Never give a child anything because they demand it or throw a tantrum for it.
Either you win each battle, or the child does. It's your choice (especially with a little 2 yr old).
I was recently watching the infomercial about the guy who sells the program on TV to control your children and he said something that made so much sense: Children need us (parents) to guide them into controlling their OWN behavior instead of letting them control us. It really is a matter of control.
God bless.