Hi F.,
Whatever rules you come up with, stick with them! Consistency is key!! Once you slide a little bit on one rule, she knows you MAY slide on others, so you cannot back down. It is very difficult, but you have to let her play out her tantrum and do not give in. When she is screaming/yelling/throwing herself onto the floor (my daughter does this too), ignore her. Or at least make her believe you are ignoring her and that her behavior is not a big deal and she will NOT get what she wants.
At this point, it seems like a control thing- she wants to see what she can get from throwing a tantrum. If it is bringing you to tears as well, she currently has the control and you need to turn the tables. When she learns that you are not giving in, then it will be time to work on eliminating the tantrums and teaching that it is not acceptable behavior.
One thing I would not worry about is her taking a step back with needing her bunny more. At her age, she is going through a time of imagination growth, and nightmares, and fears, and the bunny helps her feel secure. Plus, at this age, she is learning that she has her own will, and may tend to say/do the opposite of your request just because she is learning about herself.
Hang it there! I also just read about 'loveys' and it is really no big deal to have one. It is just something that should not be taken to school when the time comes... Many adults I know still have some form of a lovey...lol
(I need to follow my own advice - my daughter still fusses for her bottle at bedtime...lol)
Good luck,
L.