To help a pair cooperative parents answer a serious he said, she said dispute between two teenagers (they can't both be telling the truth) is a professionally administered polygraph a suitable test, or something to be avoided? what would it likely cost?
A "professionally administered" polygraph examination is no more a suitable way of resolving a "he said/she said" dispute than is a "professionally administered" astrological chart reading.
The standard technique used by polygraphers, the "Control" Question "Test," has no scientific basis, has an inherent bias against the truthful, and yet is easily beaten by the deceptive. See The Lie Behind the Lie Detector (http://antipolygraph.org/pubs.shtml) for details.