You can't. It will effect them as a matter of law. This is in spite of any diplomatic memo to the contrary. Such diplomatic opinions are arguably unenforceable at law. The U.S. Supreme Court has decided this issue.
You can permanently impact your children's right to U.S. Citizenship by deciding to seek their Mexican Citizenship. The issue of dual citizenship is thorny. There are diplomatic nuances, but as a matter of law, it is simply not allowed.
It becomes a State Department issue. If a person is arrested in another country, where they claim to hold Citizenship, the U.S. can disavow the person's claim to U.S. Citizenship. Of course, a person can go to court, but this can prove extremely costly and useless. This should be discussed with a candid and experienced immigration and nationality attorney.
Perhaps, you will reconsider whether you wish to pursue your right to Mexican Citizenship at this point.
The above is general information and does not create an attorney-client relationship.
Now from the perspective of Mexican law (where I am licensed to practice law): If you father was born in Mexico and was still a citizen of Mexico when you were born, and if you were born after March 20, 1998 (which naturally is the case), YOU ARE A MEXICAN CITIZEN BY BIRTH (article 30 of the Mexican Constitution).
Your kids may or may not be Mexicans by birth; if they are not, they qualify for residing in Mexico with you. So, there is no need for them to acquire Mexican citizenship to study and live there: either they already are Mexican nationals, or they can reside in Mexico as your dependents.
A brief note from the perspective of US law (I am also licensed to practice NY and federal law; this is clearly a federal matter): holding dual nationality should not impact US citizenship. See http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html. However, if they voluntarily acquire the Mexican nationality, it may or may not impact their US citizenship.
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