How do you handle a child that thinks spitting and sticking her tongue out is funny?

It is good that you have observed that trying to scold your daughter for these patterns or punish your daughter for them aren't going to work. Small children are likely to experiment with many behaviors which are not really acceptable--spitting or sticking out their tongues, or calling their brother a "Big Poopy-Head!"--and think that they're being terribly witty and bold. Making a point out of trying to extinguish these behaviors is generally hopeless. The more the parent makes a big deal out of the child's naughtiness, the more the child is stimulated to keep it up.

Your daughter will outgrow spitting and sticking out her tongue, because she can see perfectly well that the big important people (like you and Dad) don't do these kinds of things. Shaking your head and saying softly, "Don't do that" will convey the message to her as well as anything, and is all that you need to do. The more you make a big deal about this kind of mischief, the more keyed up your daughter will become. I'm sure that she can tell that you don't like it when she spits or sticks out her tongue. Ignoring it calmly and moving on to the next thing will help her outgrow these behaviors in time.