An unprecedented split between two Kentucky judges in the same courthouse is tangling a high-profile whistleblower case in which legislators are seeking to keep sexual harassment allegations against them secret.

Franklin County Circuit Court Judge Phillip Shepherd ruled Dec. 27 that former Kentucky House Speaker Jeff Hoover and two other state representatives can intervene in the case and reopen the deposition of the alleged victim, with whom the legislators have already entered a confidential settlement.

But in a separate and...