Trying to figure out my daughter

I know that all parents have that, "What on earth is my child thinking? Why is he acting this way? I just don't understand!" reaction fairly often. And while I know all children are little mysteries, my older daughter sometimes is more of a mystery to me than I would like.

I typically find myself describing her as "stubborn" or "a little strong-willed", and while that is accurate, it does not fully describe the aspect of her personality I can't figure out. Here is a prime example:

Last night we were playing a family game of Uno. Both kids enjoy it, and while Eleanor needs a bit of prompting, matching the colors or numbers is well within her grasp at this point. But the game goes sort of like this:

"OK, Eleanor, it's a blue 2. Do you have a blue card?" (since she can't hold all her cards, they're sitting on the table, making it pretty easy to help her out.)

She smirks, hides her cards in her lap for a moment, and pulls out a green card! She knows perfectly well it's green, but chooses it anyway.

Several times, she figured out an appropriate card to play by herself. Once, she played it in the right place...but upside down. Once, she played it on top of the deck we draw from. Once, she tried to play it but hide it under some other cards in the stack. Once, she tried to play two (appropriate) cards.

She loves playing Wild cards, and whacks them down with gusto. But when we ask, "What color do you want it to be?" she won't ever say a color. She clams up, and eventually will hold out a card from her hand and wave it at us, and we say, "OK, Eleanor picks yellow" or whatever.

She likes to deal, but after going around the circle adding cards once, she wants to switch directions. Then she wants to start in a different spot.

She wants to play. She even likes to win (though she doesn't at all mind losing). She does not want to quit...but she doesn't want to follow the social "rules" of appropriate behavior when playing a game. In linguistics, we'd maybe say that she is flouting the maxim of cooperation, or that she does not understand or care about the pragmatics of the situation.

The Uno example is just kind of cute and silly, but it really exemplifies her behavior in all areas of life. Basically, she does not ever want to cooperate or do what she's "supposed" to do. Why on earth not? This is so unlike me, my spouse, and my older son that I'm not sure how to handle it.

Often, like in an Uno game, it's not important enough to need to "handle". But envision this kind of reaction - not quite rebelling but definitely not obeying - every time you ask her to do anything: put away your toys, stop sitting on your baby sister, hold hands while crossing the street, tell me what sound that letter makes, be respectful to your babysitter. Sometimes reverse psychology does work on her, and sometimes bribery or threats work. But sometimes nothing does. And I don't want to resort to bribery or threats; eventually, shouldn't pleasing mom/dad/teacher/friends/God be a reward in itself? The intrinsic societal and spiritual reward of cooperation and obedience? (I know, I know; this is my natural people-pleaser personality talking.)

So what IS this behavior? Yes, she's three and a half; I don't expect perfection, but I also know a whole lot of other three year olds. The compliant ones tend to cooperate, the strong-willed ones will throw tantrums when thwarted. Is this being passive aggressive? Is this just a different kind of strong-willed behavior? Is she just trying to be cute, or creative? Does she just want extra attention?

I should note that I haven't noticed this behavior much when she's playing with other kids, or at least when she's playing with Miles. I also don't see it as much in class situations; she seems to listen to and more or less follow directions in gymnastics, in Sunday School, and in swimming (though it's possible her teachers might disagree with me here!) But with authority figures whom she knows well - mom, dad, grandparents, babysitters, etc. - it appears pretty regularly. Is that because she knows those people well and is comfortable with them?

And most important of all, how do I teach a child like this? How can I encourage her to obey, to cooperate? I pray that her stubbornness and creativity will turn into assets for her as she grows up; I know they can be great strengths if she learns how to harness them. But a child who does not respect authority or any kind of convention is not going to be well-liked or successful in life.

Being a "trailblazer", going her own way, being unconventional - those describe choices we make as adults that can be great life decisions. But somehow, I have to teach my daughter to function in society without society crushing her before she reaches adulthood, because a lifetime spent in time-outs and detentions and being held back a grade and being avoided by other children just cannot be good for her psyche no matter how independent-minded she is.

Advice welcome!