Read the book, Raising Our Children, Raising Ourselves. It will answer all your questions and it has a fabulous chapter on tantrums.

In short, your goal is to understand why she is so frustrated and to help her. We treat children different than adults and we shouldn't. If an adult was doing an adult tantrum (sobing, raging) we would HELP.

My personal feeling from what you are saying is that your daughter is feeling that she has lost everything.
Her home, her place in your arms, and not also going to daycare while you stay home with the baby? That's too much. The way she probably feels it is: The baby came and she is sent away. That's enough of a reason to scream day and night. Just my thoughts. Read that book.