There is root cause to her tantrums somewhere. Then sometimes kids seek attention any way they can and acting out usually works, hee hee.
Make sure she is well rested, like 11 or more hours of sleep a night. Make sure she is eating healthy which I am sure she is but that can be a factor with my kids.
The summer before my daughter turned five was horrible. The same behavior but it was stemmed from a divorce and her absent father.
I took her to a play therapist for eight weeks and got to the root of the problem, figured out a way to communicate with her and worked out a way for us both to talk about our feelings versus acting out on them. It was a life saver.
My daughter is 7 and still has the occasional fits, but things are alot calmer.
One punishment that seemed to do a turn around here at the house is the three strikes rule. I have posted it before on other tantrum issues.
First offense, like a horrible fit over something minor or hitting anyone, being defiant and sassy is warning ONE.
Next offense, straight into jammies, no matter how much of a fit, no matter what time it is, jammies on!!!!! My daughter one day had her pjs on at 1pm. It is a reminder to them how close they are to being done!!
Third offense, bed! Period, no giving in, done! She can come down for dinner if it is early, but straight back to her bed. She doesn't necessarily have to sleep but not to play, just lay there. She has screamed and cried in her room for two hours before, but I do not cave! Eventually she falls asleep.
I have to say each day has gotten better. For morning battles we set a timer for her to get ready, she picks out her own clothes and is to get ready in that time, if not, oh well, she wears whatever she has on to school. That has stopped ALL morning issues.
Giving them choices, making them accountable for their disruption and letting them know it throws the whole family out of whack is essential.
I explain to my daughter all the time, she is her little brother's example and when she acts like that she isn't doing her part.
I would make sure too with the nanny that you both are on the same page with discipline, carve out special one on one time with her each evening. I stagger my kids bedtimes so my daughter has my undivided attention after her brother is in bed.
The three strikes is a life saver here, it took a few times but she knows I am serious and I am not going to let her cause me upset or stress anymore with her tantrums.
I would sit with her when she is calm and talk to her about what sets her off, why she feels she has to act that way, what is going on with her thoughts when she acts like that.
I asked my daughter "have you ever gotten your way acting like that?"..of course the answer was No, so I explained to her that sometimes if she is feeling angry or sad she needs to walk away and find a quiet place to chill until she does something that will get keep her out of trouble.
One thing the therapist said "you cannot control your child, but it is your job to teach them to control themselves!!" that was such a profound statement to me. Teaching her that her choices are going to end in consequence for the rest of her life, good or bad. I can say lack of sleep or hunger are triggers for my daughter and my son both. Eating junk too much is another and sometimes it just comes from me getting to distracted with what I am doing around the house.
Other times, kids feel stress and need to release it, it happens, all kids throw fits. I know how upsetting and stressful it is. Just try and figure out where it is coming from, give her tools to talk about her feelings, then set very clear consequences and stick to them no matter what!
Good luck!!