You could try swatting or isolating a child every time she engages in these completely normal behaviors, but she's not trying to be naughty, so that would probably only confuse, sadden, or infuriate her, depending on her personality.
Adults interpret these actions as naughty or bratty because we want everything to flow according to our grownup training, needs, and expectations. Your baby doesn't know any of that yet, and she has a few years in which she just won't see very much from your point of view. Thats' completely normal
She is a natural scientist now, using playful exploration to find out what happens when she tries X. She's seeking to find ways to control her experience, which before now has been mostly outside her ability to control. And the tantrums are a natural outcome of becoming more frustrated than she's able to deal with.
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:
1. When she wants something, empathize. 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.
2. 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. it sounds like your daughter's sense of humor is developing, crude though it is. If you were to play "Keep Away" and laugh when she's handing you things and snatching them back, she'll get to exercise her playfulness in a way that empowers and supports her. She'll get satisfaction from that, and then want to go on to something else. She will gradually learn when such games are appropriate and when they are not from your willingness to participate. She's not there just yet.
There will also be times when you must have her cooperation, like diapering or trips to the store, so keep a special toy or two that she gets to play with only at those times.
3. 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.)
4. 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 "plan" power struggles, she will quite naturally sense any cracks in your resolve. And this is where future power struggles truly can begin.
5. Try to keep demands low when she's tired, overmanaged, or hungry. An already frustrated child doesn't have any emotional reserves left with which to cooperate.
6. Get to know her most likely trouble-spots, and plan ahead. In your daughter's case, it sounds like this is often when she wants something. Be prepared with a distraction – for example, another toy she likes when you have to take ____ 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.
7. 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 a way that feels like she's choosing it for her own good, even when there's no "if" about it.
8. 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.
9. 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. Even grownups need time and repetition to learn new things.
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 compliance, 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.
