In addition to having the proper forms of identification, for international flights, you will also find that your child or children must go through the same security screening as everyone else. This means that they will have their carryon luggage, as well as their checked baggage thoroughly examined especially at international airports in usa. This examination may include an x-ray screening or a hand check.  Should a problem arise, they will likely be pulled aside, like any other passenger. The only difference is that you should be able to accompany them, if and when this does occurs.