Polygraph tests are generally not used in family law matters. The best way to expose a liar is hire a good attorney that can untangle the web of lies made by opposing party.
My recommendation would be that you obtain a free consultation from a family law attorney to review your case before taking action.
Judd S. Nemiro
Law Offices of Judd S. Nemiro, PLLC
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Generally, a polygraph test would not be used in a family law case. It is up Judge to determine the credibility of a witness. Thus, the Judge would evaluate your testimony, as well as the testimony of the opposing party. Ultimately, the Court must make a determination regarding what is in the best interest of the minor child(ren). It is recommended that your consult with a family law attorney to fully evaluate your facts and circumstances, and determine the best course of action.