What worked with the Cool Niece (she's 2 1/2) was ignoring the tantrum. Walk away and let her scream. Pretend she isn't there, there is no noise, and you are going about your business. It's hard to do that - you'd like to toss her in her room or give her what she wants - but that just means the the behavior is reinforced. If getting Mommy's attention consists of tossing her into her bedroom, then she wins. She has met her goal.

Periodically she'll try the tantrum thing - you can see her calculating if it's worthwhile to do it. She's doing it less and less though, what she gets out of it is...nothing at all. No benefit, no behavior.

You could also make sure that being sent to her room is NOT a fun thing. This means that there should be nothing in there to entertain her. No radio, stereo, television, computer, phone (I know she's a little young for some of that stuff), toys (put the box in the hall for awhile), NOTHING that will help her while away her time except maybe a stack of books.

My mother (infamously) would supply the kid being punished with the vacuum cleaner, Windex, and paper towels with the admonition, "You know what to do."

If getting sent to her room means she'll be spending time bored out of her mind, she'll give up the tantrums.