A child (under 18) of a USC who has permanent resident status in the US, is in the custody of the USC, and is under 18 is actually a US Citizen (or becomes one when the parent becomes naturalized). Look up section 320 of the immigration act (as amended in the late 90's or early 2000's) and download form N-600 (and read the instructions). It's the automagic pseudo-naturalization process for children.
For example, my wife naturalized last June (six months before me - long story). My daughter had a GC, was living with us and was 17 years old. She became a USC as my wife finished her oath. She had a US Passport 2 weeks later (before my wife (she was traveling very soon afterwards)).