How can I handle the immigration proceeding for a child of a US Citizen?

Although, I cannot say for sure, it is possible your daughter may already be a US citizen out right by operation of law. If so, she may not need a green card. I am unable to say categorically one way or the other since you did not provide sufficiently detailed background information about your case including the dates of marriage, your daughter's date of birth in Mexico as well as the date of your naturalization. You should speak with an immigration lawyer and provide the lawyer all necessary biographical information. It is only after determination has been made that US citizenship has not in fact devolved on to your daughter should you then consider an application for legal residence for your daughter. I doubt that you can make this determination without the assistance of a competent legal counsel.

I have good news for you - and not so good news, too. The good news is that your daughter does not need any immigration proceeding. By law, she is a citizen of the United States from birth. The only trick is to get the Immigration Services to agree with this statement. And, by bringing your daughter into the U.S. illegally, taking her back to Mexico, and then bringing her back into the U.S. on a school card, you broke enough immigration laws to make your daughter's case difficult and to put yourself in danger of being stripped of your permanent residency and deported. So now, you need a lawyer - and that's not such a good news, because it will cost you much more time, money, and aggravation than it would have if you consulted an immigration attorney before starting to act. So I would strongly recommend that you talk to an immigration attorney now, before the case is made any worse. (If you already have an immigration attorney, and did everything you have done so far on his/her advice, get another attorney, a real one).