Have come back to this, hoping you got some sleep!
I have 3 children, so have some experience of sibling jealousy. IME, I think half the battle, with all child rearing issues, is to see the situation through the eyes of the child. Also, it is important to have realistic expectations of behaviour, based on the age and development of the child. I hope that makes sense.
Imagine, for a moment, that you have been married to your dh for 6 years. During that time he has loved, nurtured and cared for you.
Then, he brings home a new wife. She is younger, prettier and seems to be the centre of attention. How would you feel?
Sorry if that sounds preachy - it isn't meant to, I just think it helps to find solutions if you approach situations from the child's POV.
That is why I really don't think punishments like smacking etc are helpful. Your dd is jealous, she is trying to push the boundaries to get your attention, and looking for reassurance that she has not been "replaced".
Of course the baby needs lots of time and attention, but it is possible to show your dd that her life is fun and interesting, and how much you appreciate her, whereas being a baby is actually quite boring - babies can't run around and play, can't have interesting meals/read books/draw etc.
Does any of that make sense?
Maybe seeing it from her POV will help you to come up with some strategies.
You may find that she will regress quite a bit - this is normal.
Going back to school may be traumatic, (she will resent being "sent away" while ds stays at home with you) but OTOH she may at least be more tired!