Tantrums...I notice you are a working mom so that means both your kids are in daycare right? I would go there first and find out how her behavior is there and how things are handled. I know working moms don't like to hear this but it's the truth...the daycare workers see her more than you do and they are the ones molding her behavior more than you are. Now, I say that because (I'm a behaviorist so bear with me) if 8 hours a day, 5 days a week anytime she wants something she is getting it, or she's able to just take things or her tantrums are handled a certian way or whatever it may be, then 1.) that's reinforcing behavior 2.) she's used to certain behavior and 3.) you absolutely need to know how it's being handled there. Don't take their word for it either. Often they will sugar coat things for parents so I'd try to have some time where you can observe her and the workers without them knowing you are there. The fact that they spend so much time with her means they are a significant influence on her behavior. You want to know what form that influence is taking.
OK, next thing. She's 2. Two year olds tantrum that's what they do. The reason for a tantrum is this...she wants something and you aren't giving it. Either attention, a toy, food, or more importantly, you don't speak her language. Again I go back to daycare. If they are using words that you don't use or hand signals etc...even inadvertantly that can cause her frustration as she tries to use the same set of expectations with you but you don't get it. (See where I'm going? Please know I'm not slamming you for being a working mom or anything...just trying to talk you through the behavior pattern.=) ) For example, say that in daycare they use the word "cup" for "sippee" and you don't know that. She is using a word that the daycare workers know to be "cup" but they haven't told you this (maybe they forgot to mention it or think you know) and so she's saying this to you but you don't know what she means and since she's two she's unable to be more expressive and BOOM there's your tantrum. So that's one area to look at.
Children in daycare are often on a schedule. Some children do very poorly with the lack of a schedule when it's absent. If she's dependent on knowing that 11 am is snack (because let's face it, most of her time is spent at the daycare not at home) and then the weekend comes and she can't count on the stability of the schedule anymore that can lead to frustration. If at the daycare she's being indulged because she's cute or a favorite child or it's a small place and generally she gets what she wants then she learns a little fussing gets reward. When something like that works, then when that stops working for whatever reason, the behavior escalates. (For example, you have a brand new car, and because the car always starts everytime you turn the key, that's your expectation :the reward for key turning is the engine comes on: but one day it does not start. You turn the key once and it doesn't start. You turn it again, still nothing. How long will it take you to begin turning the key over and over and then cursing and swearing in frustration?) So, you absolutely must know how her wants and needs are being tended to in daycare so you can either fall more into line and fulfill her expectations or get the daycare to fall into line with your expectations you know?
As to the tantrums themselves, there are many schools of thought on this and I'll just tell you what I did. I would tell my son "I know you are mad, but I don't want to see this so you can go to your room until you can be nice." And I'd put him in his room with the door open (washcloth placed over the top of the door or in the hinge space so he couldn't slam it and catch his fingers, and put a baby gate up in the doorway. This way he was not "cut off" from the world, he was given permission to feel what he was feeling, because let's face it, if she wants a cookie and you say no, you've pissed her off. That's legitimate. I see no benefit, and in fact long term harm in dismissing the emotions of children. So I acknowledged my son's emotion but at the same time let him know that while it was OK to be mad, I was still in chage and I didn't want to watch the tantrum. And so depositing him in his room worked. I only had to do it a few times and the tantrums stopped. HOWEVER, and this brings me back to daycare...if she does this there, and they give in then you have a much steeper climb. Giving in to a tantrum especially only every now and again (it's called variable reward scheduling) helps to set a behavior in concrete. So you really must find out what they do and insist that they handle things your way. Otherwise you will see more and more of these not less.
Other people cuddle children during a tantrum etc...but I see that as rewarding the bad behavior. I want to extinguish the bad behavior not reward it nor use aversives if I can help it. (Putting the child in her room would be an aversive though.) Alternately, if you can just ignore the tantrum, like stepping over her and not making eye contact etc...you can leave her where she falls. Any attempt to engage her when she's tantruming encourages the tantrums and in fact encourages them to be longer, stronger and more frequent. (Because it's a variable reward schedule.)
**Here's the ugly part of variable reinforcement. Let's say we have a 4 yr old that tantrums. I want the tantrums to stop. So I decide to take the ignore it path. (Extinction) But while I'm waiting for the behavior to extinguish the tantrums are going to continue and will probably get worse. If this 4 yr old can get me to give in just once...she has put herself on a variable reinforcement schedule. She now knows there is a magic threshold where I will break and she will get what she wants. She is going to work harder (tantrum more, louder, in embarrassing places) to get me to give in. If Heaven forbid I happen to give in a second time, the tantrums are sure to continue and only escalate.**
Finally, when she does it in public you MUST be prepared to just grab the kids and leave. I know that's hard. "But I need groceries!" Yeah I know...believe me. I lived it. My boys are 23 months apart. But trust me on this. If you say to her before you go in "I expect you to...(and be very concrete in your language don't just say Be good) sit in the cart nicely, not fuss, not cry and No screaming or we will leave." Then be prepared to back it up. You have to. Or otherwise she learns you can be bent to HER will and the tantrums will get worse. Arrange a sitter, or get off work one hour early to do your shopping or go in the middle of the night while they sleep. Figure out a way to just get the shopping done without them if you have to. The other part of this is to make sure you aren't going when she's tired or hungry or any of the things that will make her more likely to tantrum. And finally, I would be prepared with tiny rewards for all behavior that is not the behavior you are trying to eliminate. So if she is sitting there quietly, just hand her a sticker. If she asks why tell her "because you are sitting quietly so Mommy can get her shopping done." And then a few moments later another. (food works too although then you may start a pattern you don't want to later have to break.) But small rewards MUST be given in a pretty steady stream with 2 yr olds to get them to "get it" and in this way you might be able to actually finish your shopping BUT and this is VERY important...YOU MUST NEVER EVER EVER use bribery. "If you are good then you will get a Barbie" Bribery will always fail eventually and when it fails the results are spectacular. For example, you tell her "If you are good while I shop then you will get a Barbie." and then she's not good...now you have to say "No Barbie" and in fact we love to use threats like this with children. So now not only is she pissed that she can't have the pink cereal now you've take away her imagined Barbie. She will explode. Never do this. (Actually you can do this when she's older and has a concept of time and the ability to be patient. So the 16 yr old can get the "be good this week or you can't use my car on the weekend" but there will still be a tantrum =P)
I hope some of this helped. Please know I know what you are going through. These are sound behavior principles and will work but will take time. Do check to be sure she's not being "spoiled" at daycare though because that will only make your job harder. Also if you have another adult that spends a lot of time with her (husband, SO, parent whatever) make sure they don't give in because it's easier. Everyone in this child's world must give her consistant feedback and level expectations so that she knows what to expect of the world and the people in it and she can predict the behavior that is expected of her. At 2 she doesn't have a concept of right and wrong only "getting in trouble" really so we have to try to be fair to her too.
Good luck! These are hard times (having two littles that close together) but believe me you are paying the piper now, they will play together a lot. You'll be glad eventually, but it took me a long time to get to where I was glad. My youngest was about 4 before the boys consistantly played together and so you've got a ways to go and lots of challenges ahead. Additionally, the 1 yr old is watching all this go on and is learning how to behave. So keep that in mind!
*comfort to you Dear*
K.