I think girls to be just as aggressive as boys, but in a different way. Does God allow mean behaviors such as being manipulative and subversive to get what one want? Please tell me, how do you turn around a catty, snippy or snooty child?
Oh, I agree; aggression can be demonstrated in different ways. And, yes, the ways girls tend to demonstrate bad behavior are usually different from boys, just as girls are different from boys. Yet bad behavior remains just that -- bad.
What you are describing is called craftiness, cunning, backbiting, and whispering in the Bible.
Whispering is talking about others behind their backs. "All who hate me whisper together against me; against me they devise my hurt. "An evil disease," they say, "clings to him. And now that he lies down, he will rise up no more." Even my own familiar friend in whom I trusted, who ate my bread, has lifted up his heel against me" (Psalm 41:7-9). Whispering is the wedge that drives friends apart. "A perverse man sows strife, and a whisperer separates the best of friends" (Proverbs 16:28). It is found listed among various sins in II Corinthians 12:20.
Backbiting is slander. It is the attempt to bring a person down by talking evil about them. It too is found listed in II Corinthians 12:20 as well as in Romans 1:30. Backbiting stirs up trouble, causing people to become angry. "The north wind brings forth rain, and a backbiting tongue an angry countenance" (Proverbs 25:23). You cannot be righteous and have a backbiting tongue. "He who walks uprightly, And works righteousness, And speaks the truth in his heart; He who does not backbite with his tongue, Nor does evil to his neighbor, Nor does he take up a reproach against his friend" (Psalms 15:2-3).
Craftiness and cunning is the act of manipulating people through deceit. In other words, it is a form of lying. "Everyone will deceive his neighbor, and will not speak the truth; they have taught their tongue to speak lies; they weary themselves to commit iniquity" (Jeremiah 9:5). It is a shameful act. "But we have renounced the hidden things of shame, not walking in craftiness nor handling the word of God deceitfully, but by manifestation of the truth commending ourselves to every man's conscience in the sight of God" (II Corinthians 4:2). On motivation for craftiness is to gain the upper hand over a perceived opponent. It is a way of oppressing those you do not like. "A cunning Canaanite! Deceitful scales are in his hand; he loves to oppress" (Hosea 12:7).
Obviously these are character traits which we don't want developing in our children. How do you handle such a problem? First, recognize that it is being done for personal gain. You need to figure out what the child is hoping to accomplish and then make sure that she doesn't benefit from her manipulations. This is what God does. "He frustrates the devices of the crafty, so that their hands cannot carry out their plans. He catches the wise in their own craftiness, and the counsel of the cunning comes quickly upon them" (Job 5:12-13). Second, since at its core craftiness is an attempt to overpower others, counter it in your punishments by having the child do good deeds for which she is unable to gain any return. "But I say to you who hear: Love your enemies, do good to those who hate you, bless those who curse you, and pray for those who spitefully use you. To him who strikes you on the one cheek, offer the other also. And from him who takes away your cloak, do not withhold your tunic either. Give to everyone who asks of you. And from him who takes away your goods do not ask them back. And just as you want men to do to you, you also do to them likewise. But if you love those who love you, what credit is that to you? For even sinners love those who love them. And if you do good to those who do good to you, what credit is that to you? For even sinners do the same. And if you lend to those from whom you hope to receive back, what credit is that to you? For even sinners lend to sinners to receive as much back. But love your enemies, do good, and lend, hoping for nothing in return; and your reward will be great, and you will be sons of the Most High. For He is kind to the unthankful and evil. Therefore be merciful, just as your Father also is merciful" (Luke 6:27-36). Require your daughter to spend time doing good for someone else for no pay. If you can arrange it so that those she doesn't like end up as beneficiaries, even better.