Sounds like a typical three year old to me! Three was much worse than two for both my kids, and most of my friends agree it was with their kids too.
They are more verbal so they argue, and they push more limits because they are feeling more sure of themselves. And they whine, oh my goodness I thought I was going to go nuts with the constant whining!!!
Now is a good time to implement a discipline strategy, together with your husband, with predictable repercussions and stick to it. I used a book called "Making Your Child Mind Without Losing Yours" and I liked it a lot. It's based on logical consequences. She won't sit down at dinner, dinner is over. She breaks a toy, toy is gone and she doesn't get another. If you're out to dinner and she's acting up, someone takes her to the car until she calms down. No, it's not fun for you, but eventually she'll learn she has to listen.
Good luck, and remember it will pass!