I think the best approach would be to challenge the validity of polygraphy in general as the primary argument. Polygraph "testing" has no scientific basis at all. The fact that you "failed" and the father "passed" is evidence of nothing.

Your lawyer may wish to submit into evidence Professor William G. Iacono's article, "Forensic 'Lie Detection': Procedures Without Scientific Basis":

http://antipolygraph.org/articles/article-018.shtml

Also, there are a number of scientific experts on polygraphy who may be able to provide rebuttal testimony. I will send you their contact information in a private message through this message board.

   I really need some good sound advice here.... I am in a major custody battle right now. My 4 year old child accused his father of fondling him.DCF unfounded the allegations, spoke to the DCF director re: this, he said because lack of phyiscal evidence and no admittance to wrongdoing by the father. ( if a child is fondled especially a male would their be phyiscal evidence ??) Counselors/social workers  felt he was indeed molested though , I took a polygraph and was asked if I made my child lie about the allegations, if my child actually said these allegations, and have I coached my child into saying these things. Mind you prior to the polygraph 3 minutes prior I had a guardiam at litem screaming at me about how I am going to lose my son and I am a liar. So I took the damn test, with extreme anxiety, shaking in my seat, unable to sit still, my feet dangling from the chair as I could not reach the floor, and in this big leather seat which I could not get comfortable in. I answered all questions honestly and failed!!!!!!!!!Now the polygrapher is going to trial against me to accuse me of being a liar, the father passed as they said with flying colors, and that day was as cool as a cucumber, which I suspected something was up he usualy has a nervous twitch but low and behold that day he had none, quite amazing!!! anyhow how can I rebuttal the results, I do have a lawyer but any help would do, I am willing to take another confidential polygraph  test. This is a matter of losing custody to a very sick individual, we agreed to the polygraph so they are admitting it in court but now I must fight the results with the best fight possibly, any suggestions would help... thanks