All of this is normal, and some littles are more 'normal' than others. She's only slowly developing impulse control, and believe it or not, she'll probably be a cooperative and patient child in two more years. Right now, life is giving her lots of things she has to wait for, and if you can help keep her frustration levels at a low roar, she will gradually learn that patience is the way to go.
This is an extremely frustrating time in a toddler's life. Most of her time is managed and scheduled by big people who don't see life from her perspective. She sees so many things that she wants to do and touch, and is not allowed very much of it. And when she does get to hold something, she may not yet have the ability to interact with it in a satisfying way. So she's frustrated a good part of every day.
Punishing her for being frustrated will only make her more frustrated. Helping her interact with all that fascinating stuff will help satisfy her need to understand and explore and manipulate.
Here's my favorite list of often-successful tips for managing your daughter over the next couple of years:
1. Your daughter 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 experience and control to make most of life meet our grownup expectations. Your toddler doesn't know any of that yet, and she will probably have a couple of years in which she just won't see very much from your point of view. Thats' completely normal – she can't help it.
3. Digging in heels and tantrums are a natural outcome of becoming more frustrated than they're able to endure. Many parents report that this "new" behavior seems to come out of the blue. The stress of travel and changing schedules, or illness, or any major change, may contribute.
4. Though you won't ever have a toddler who can behave like an adult and make all the choices you would make, there are tried and true methods for eliminating much of the mutual frustration that the mom and the child experience during the next couple of years. This may be challenging when you're busy, but overall, you'll expend less time and energy than you would if dealing with behavior that isn't evolving in a positive direction.
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 to a child. They hear no so often, and they can be so frustrated. So look for ways of finding a mutual "yes," and save "no" for those occasions when children are trying something dangerous.
5. Keep it playful. Children lean 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, crude though it may be. (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" outlets for those repeating behaviors.)
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.
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. Children absolutely hate unexpected transitions. 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 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. And be calm. Desperation will show, and even though she's too young to deliberately engage in a planned power struggle, she will quite naturally sense any cracks in your resolve. 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.
10. Get to know her most likely trouble-spots, and plan ahead. For many kids, it's when they want some tempting object or food 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 junky 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 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 your stress and hers.
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. 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 scared, shocked, 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. Children seek attention and approval, and if she knows you're noticing her good 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 both well. Enjoy this magical and all-to-short time in your daughter's life.