Generally speaking, results from lie detectors are not admissible in court (at least not in criminal cases).
But why put yourself through that? Haul the little twit into court and get a court order that she go forward with permitting visitation. Put the onus on her to explain what concrete evidence there is showing your husband is a danger to his daughter. The fact that there is no medical evidence will help your case (subpoena the doctor or subpoena the medical report).
Has she put the child in counseling? If not, you can argue that she is merely delaying visitation – obviously if there was a real fear, the kid would be seeing a professional. If the kid is in counseling, get his records.
Most likely the ex is doing to your husband what mine tried to do to me – raising fears that the child would be harmed by behavior but not submitting the child for professional care which would clearly refute the allegation.
Polygraphs are not perfect – but by making your husband take one, she is putting him on the defensive. Put HER on the defensive.