P.M.
Child behaviorists make a very compelling case that ALL behaviors are strategies to get some need met. Your daughter is feeling some need that is not being met when she's acting out, and the more carefully you can ferret out what she's feeling the more likely you are to help guide her toward better behavior.
Keep in mind that personality does make a difference. Some kids are definitely more intense, more demanding, more needy or bossy or energetic than others. Your daughter may be one of those. And the "family rule" definitely works against you. Children, particularly the more intense and demanding ones, must have opportunities to gradually learn to deal with disappointments.
Very few 2yo's have any real idea how to share. They may tolerate having things taken from them, or being required to hand over toys to other kids, but that's not the same thing as understanding the reciprocity of sharing. Also, 2yo's are still at the stage of "parallel" play, playing alongside other littles (and perhaps grabbing their toys), but playing "with" will only begin to develop gradually over the coming year or so. If it's possible, keep the two kid's play spaces somewhat separated from each other as often as possible until they show an interest in cooperative play.
You can't "make" a child be happier or more easy-going, but you can often manipulate their experiences so they are less frustrated. This is a very difficult age for most kids, who want to do/try so much more than they are able. They are limited by motor skills, by basic comprehension, by language skills, and by rules and schedules that they have no say in controlling.
Here's my list of favorite tips to make toddlerhood easier for mother and child. I hope you find some of these ideas new and helpful:
1. Trust that she is not "trying" to be naughty. Children don't really want to cause problems or get in trouble if they have any other way at all to meet their own growing need for autonomy, independence, and control of their circumstances.
2. Adults have the self-control and experience to make much of life meet our grownup expectations. Your toddler doesn't know any of that yet, and it will be a while before she sees very much from your point of view. As exasperating as that is for you, she can't help it. It's just reality, and reality is easier to take if you can accept it.
3. Digging in heels and tantrums are a natural outcome of becoming more frustrated than the child is able to endure. This "new" behavior may seem to come out of the blue. The stress of travel, teething, changing schedules, illness, or any major change, may contribute.
4. When she wants something, empathize. Big time, and in the child's language. I love the advice of Dr. Harvey Karp on how to get on a tantruming toddler's wavelength in this and several related videos: http://www.youtube.com/watch?v=G6KnVPUdEgQ&feature=re... . Once your little girl realizes you do care about what she wants, she's more likely to be able to calm down and cooperate with what you need from her. And there are lots of positive ways to approach this, rather than just saying no. They hear no so often, and they can be so frustrated by it. And they learn to tune it out. So look for ways of finding a mutual "yes," as in "Hey, look at this cool toy," or "Can you hop over to me like a bunny?" instead of "No, don't touch that," or "Stop that and come here right now!" Try to save "no" for those occasions when children are trying something dangerous.
5. Keep it playful. Children learn primarily through play. You may need help with this if your parents didn't model a lighthearted and cheerful approach when you were little. The book Playful Parenting is a great resource. Your daughter's sense of humor is developing, and you'll both be happier if you can nurture that. (Also be aware that some "behaviors," like throwing, are a natural experimental activity for kids, a form of play that is programmed into them for the purpose of developing brain/body connections. Find plenty of "acceptable" play outlets for those repeating behaviors, like throwing things into a basket.)
6. There will also be times when you must have her cooperation, like diapering or trips to the store, so keep a special toy that she gets to play with only at those times or keep her as playfully engaged in the process as possible. This often requires creativity, because each child is different.
7. Here's a big one: give advance notice when you'll want her to be doing anything differently, especially when she's grooving on her activity/play. All children absolutely hate unexpected transitions (and so do most adults). With my grandson, we let him know at least a couple of times that a change is coming ("We're going to go to the store / have lunch / take a nap pretty soon." … and then a second or third alert one minute before making the change.)
8. Whatever the next activity is, make it sound as desirable as possible. Give some detail about the ride in the car, or a favorite food at lunch, or sweet snuggles before nap. Be positive and enthusiastic. Be calm. Be "as inevitable as the tides." Desperation will show, and even though she's too young to deliberately plan a power struggle, she will quite naturally sense any cracks in your resolve in an attempt to meet her own emotional needs. And this is where future power struggles truly can begin.
9. Try to keep demands low when she's tired, over-managed, hungry, or sick. An already frustrated child doesn't have any emotional reserves left with which to cooperate. (Often true for adults, too!)
10. Get to know her most likely trouble-spots, and plan ahead. For many kids, it's when they want something they've seen. So keep those things out of sight when possible. Baby-proof your home. Be prepared with a distraction – for example, another toy she likes when you have to take something away from her, or a healthy treat when she wants a sugary snack. Laughter, introducing a new game, a few twirls and bounces, hugs or tickles, a goofy song, can help break into her determination to get something she wants (that short attention span is both a curse and a blessing).
11. Avoid bribes, but let her work toward occasional rewards. Don't try to "buy" cooperation for things she must do anyway with "IF you'll do X, we'll let you have Y." Instead, phrase it as if she gets to assist in advancing something good for herself: "Hey, as soon as you help me get X done, then we get to do Y." It sounds like a small distinction, but it's important. It gives the child a chance to cooperate in what feels like choice, even when there's no "if" about it.
12. Be sure she gets lots and lots of physical activity during the day. Time outdoors in nature is calming for most children. If she has pent-up energy, it will have to come out some way, and unless channeled in a positive direction, it will likely to add to both her stress and yours.
13. Whatever you are trying to teach will need to be repeated hundreds of times over the next few years. That's completely normal. Attention spans and impulse control are extremely limited in toddlers. It takes time, attention, and repetition to build new habits. Look at your parenting contract, and you'll find it in tiny print under "I agree to the following terms and sacrifices."
14. Spanking and time-outs don't work for every kid, and will sometimes actually backfire over time. Especially with spanking: children may be shocked, scared, or shamed into cooperating, but behaving for the sake of avoiding pain isn't the same thing as developing an internalized sense of "good." Consistent, calm guidance and demonstrations of what you DO want from her will work better in the long run than punishing for what you DON'T want her to do. See more on this by googling The Science of Parenting or Emotion Coaching.
15. Pay attention to what you love and appreciate about your daughter, and make sure she knows. Remind yourself to do this even when you're tired or busy. Children crave attention and approval, and if she knows you're noticing her finer moments, she'll try to create more of them. If she doesn't get that positive notice from you, she'll seek attention in other ways, and that often turns out to be misbehavior, because you notice it.
I wish you all well. This stage won't go on forever. I hope you find a great deal of pleasure in this unique time in your daughter's life.