How can I prove that I am telling the truth in mediation?

I am having a lot of issues with my ex-husband lying in court. I have lost my children temporarily due to his fabricated stories. I need to know what I can do about this. My children are suffering, and we need to fix this problem. Is a polygraph test available in mediation? Does anyone know the laws about what I can do with him lying in mediation? I have done plenty of research but cannot seem to find a significant answer. Please help us; thank you.