You don't mention it in the description of your issue, but I noticed in the 'A little about me' section, you have a 3 month old son as well.
Yes, part of this is 2 year old behavior. They push boundaries, they will drive you nuts and you DO have to stand firm. However, my instinct says this is exacerbated by the new little one. Your daughter was the center of attention for almost 2 years. She got ALL of mommy's attention and ALL of daddy's attention. Now, she has to share. 2 year olds are NOT good at sharing.
It seems like your daughter is trying to get your attention.... and that she has determined the only way to get your undivided attention is to make these bad choices.
Also, toddlers have some big emotions. They can do more things, but not everything they want to do. They are introduced to other kids and the whole sharing thing and not wanting to give up their toys etc.... Many times toddlers have these big emotions, but they don't know what they are... and they don't know how to deal with them. That's where Mama and Daddy step in. We need to vocalize for them what they are feeling, which I think you're doing. And then we need to demonstrate how to handle these things.
One thing you need to be careful of is not over explain a situation. I think the 'you can't have a cracker right now because it's almost dinner time and we don't want to spoil your appetite' explanation is a little long. Remember... toddlers = short attention span theater! You may want to cut it down to something like "I know you're hungry, I'm making dinner right now."
My husband often tries the long explanation thing with our 2 year old... about 1/3 of the way through I see her eyes glaze over and she isn't paying attention to a thing he is saying. Sometimes he catches it and will ask 'are you paying attention' ... she'll be honest and say 'NO!' ha ha ha
I would say yes, the temper tantrum would warrant a time out. I would approach it with 'Temper Tantrums are a bad choice. Now you will get a time out because you made a bad choice.' Remind her that good choices are to be gentle, not to scream, not to stomp your feet.
It is also important during this time to ensure that when you are with her, that YOU are demonstrating good choices. If something doesn't go how you hoped it would...how do you react? Toddlers model everything we do. I'm not saying you act out, I'm just saying sometimes we forget that our toddlers have transitioned into this 'copying mode' ... virtually overnight. :-)
I would also try to ensure that your daughter is getting good one and one time with your and your husband. She may be feeling left out... or forgotten. Not in REALITY... but in HER mind. So, one on one time will help with that. In addition, toddlers love to help. Find ways she can help with the new baby ... this will help her to see that you are one family... helping each other and everyone has a place in the family.
Hope this helps! I'm not a psychologist or anything, but my sister is a Social Worker whose specialty is childhood development. We've had MANY of these conversations... these are just some of the things I have gotten from her.