Ditto on the ignoring the tantrums and giving her praise when she does behave well. You might also want to spend some time alone with just the two of you...I know it's hard to do when you have a baby but probably part of the reason she is acting up is she misses her time alone with you that she had prior to the baby showing up.
On the ballet thing, some kids just aren't ready for it until later. It's a very structured environment, my daughter started at 3 and took to it like a duck to water but my niece didn't get into it until she was 5. Her mom tried earlier but she just wasn't ready to concentrate on it.
And just remember 3 doesn't last forever...pretty soon she will be a teen.