I am sorry to hear of this. I cannot say why CPS insisted that the state drop criminal charges against your daughter, because I do not know what the results of their investigation showed.
What I CAN tell you, however, is that you certainly may act in self-defense against a minor if you have a reasonable belief that you are in imminent danger of death or serious bodily injury. The fact that the minor is much younger than you are and your child, at that, does not make a difference.
That said, self-defense is an affirmative defense. That means that it is a defense that must be asserted at trial. If believed by a jury, self-defense is a complete defense and it can get you acquitted of the charges. However, self-defense must be proved and so it would not prevent an arrest.
Here, you're not denying that there was contact. So you can be arrested for that. Whether it is justified under your state law is a question of fact that will be decided after the close of all the evidence after the case goes forward.
Get yourself a lawyer and show him all you've shown me. It sounds as if you have a strong self-defense case.