I love Laurie's post! (I frequently love Laurie's posts, btw!)
I will add to the last one she said about whining. Tell her ONE time that you don't understand whining. If she wants to talk to you, she has to talk in her big girl voice. And then ignore every bit of whining. Make it as if she is not talking at all. As soon as she starts using a non-whining voice, "turn on" and answer her THEN. She will learn that whining gets her nowhere.
If I were you, I'd buy a pair of earplugs to put in your ears for when she is screaming in the car. That is ONLY for if you have a deadline and will be late. Otherwise, I'd stop the car in a safe place, get out and shut the door and make her be by herself to do all that crying and screaming. You can read your phone and act like you don't care.
I will tell you that anytime my kid did this, he was in his room in a flash and not allowed out until there was no more tantrum. If we were somewhere else, out and about, I dropped whatever it was, even if I had a cart of groceries, and took him to the car and buckled him in. Even if he was kicking and screaming. And then I told him we weren't going ANYWHERE until he had straightened up. I would stand outside the car until he stopped. Then I'd open the door and say "Are you ready to behave?" If his tantrum was EVER over wanting something, it was a sure fire way to guarantee he wouldn't get it, that's for sure!
Honestly, I was working and there was NO way I'd let a tantrum make me late for work, so I was very business-like with my kid. He learned, given time, that he couldn't get away with any of it. I was tough. Given that she is pushing buttons really hard (that thing with your husband near his eye is REALLY pushing the envelope), I think you should be tougher with her until she gets it. And it might take a while, but absolute consistency and loss of fun, especially if you are at the park, library, store, pool or whatever, should help her learn to start thinking about the consequences of her actions. Good luck!!