This is normal behavior, though your daughter sounds more spirited than some. She doesn't really want to cause problems, she's trying to meet her growing need for autonomy, independence, and control. This spirit and energy will help her get ahead some day.
Busy parents want everything to flow according to our grownup expectations. Your toddler doesn't know any of that yet, and thats' completely normal – she can't help it. Digging in heels and tantrums are a natural outcome of becoming more frustrated than she's 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.
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. It takes some thought and planning, but you'll expend far less time and energy than dealing with behavior that isn't evolving in a positive direction.:
1. 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.
2. 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.
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.
3. 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.)
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 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.
5. 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.
6. 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. Be prepared with a distraction – for example, another item 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 (that short attention span is both a curse and a blessing).
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 what feels like choice, 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. Look at your parenting contract, and you'll find it in microscopically-tiny print under "I agree to the following terms and sacrifices."
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.
I wish you both well. 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.