The court document states a deposition was scheduled for Wednesday, but Hunter backed out for a second time.
The motion also says Hunter would not agree to answer questions under oath unless the transcript was sealed to "protect her privacy."
Young's motion points out Hunter answered personal questions for "GQ Magazine" and posed for pictures "partially undressed."
Hunter is suing Young to get back a sex tape that allegedly shows Hunter and Edwards. The tape was left behind in a house in Chatham County where Young and his wife lived with Hunter.
The existence of the tape came to light after Young's book "The Politician," hit the stands in February. In the book, Young documents his years working for Edwards and talks about his role hiding the existence of Edwards' affair with Hunter from the media while he ran for president.
Hunter sued the Youngs for invasion of privacy and demanded the tape back. The Youngs were ordered to turn over all copies of the tape and other material to the court while it determines ownership.
Young admitted there are some missing items he can't account for, but says he has given the court everything it has requested.
Last month, attorneys for Hunter said the Youngs have held back copies of the tape.
The Young's lawyers have argued that she gave up ownership of it by abandoning it and not trying to claim it for several years.