D.B.
Go down to the library and go to the parenting section to learn about tantrums.
She is only 3 so she is saying "I hate you mommy" or blaming you for stuff with not sense of a) what hate means or b) that it's completely illogical because you weren't even there. You can't talk her out of it with logic at this age, so don't try to explain that you weren't around at the time. She's frustrated and doesn't understand "life" - you're there, so it must be up to you to fix things, in her mind.
The best thing is to ignore this behavior. She keeps doing it because you are engaging with her and because she gets a payoff from you - attention or a cookie or help getting the Legos apart or whatever. So perhaps you need to reevaluate your reactions and change how you react.
That said, she may have some additional problems with frustration and anger. It does seem to me that she has trouble settling down - at night, after something doesn't go her way, etc. I imagine she's not sleeping well. Start from the premise that she is unhappy - and find out why. Does she not have the vocabulary to express needs/frustrations? Does she not have enough varied stimulation to occupy her and wear her out? Does she, on the other hand, have TOO MUCH stimulation and not enough quiet time, so she can't self-soothe. I do think you might look for additional resources, either with a second opinion to rule out any medical anomaly or behavioral issue, and otherwise to see if you can work with a parenting or family therapist to help you "read" your daughter better, identify her triggers, and come up with totally consistent techniques to reward good behavior and redirect undesirable behavior. At 3, you really don't want to talk about punishment, but definitely about redirection. Find out, either through a family therapist, your pediatrician, the town's office of children and family services, or a good reference librarian, about parenting classes and resources in your community.