I like ClothCrazyMom's advice!
Just wanted to let you know that you are not alone. My dd1 is a few months older than your daughter, and we occasionally get some of the behaviour you are describing.
When dd1 talks disrespectfully, we tell her that she may tell us that she is angry/upset/etc, but that she needs to tell us in a nice way, and then we can talk about whatever the problem is (then model a polite way to express disagreement).
This never seems to do much at the time, but then she will express disagreement nicely at other times (sometimes!), so I do think it is slowly sinking in.
The following us screaming - that doesn't happen too often, but if she does that, I ask her (or carry her, if she refuses to go) to go to her room, explaining that I know she's upset, but that it isn't fair to everyone else to have to listen to the screaming. That as soon as she's able to tell us without screaming what is wrong, she may come back down.
She will sometimes come back down still screaming! In which case, I just take her back upstairs again and explain that we really do miss her and would like her company, but only when she can stop screaming, as that hurts everyone's ears.
Haven't had to do that in awhile, but back when we were doing that, we sometimes had to carry her back to her room 4-5 times.
I think the trick is to stay calm and give them appropriate ways to express their frustrations/upset/etc. Sometimes dd1 can't process all of that when she is upset - so we revisit things later, talking about better ways to express our feelings/etc.
Hang in there - it will get better!