It also names her brother-in-law, Warren Hance, who owned the child-packed minivan Schuler was driving.
A copy of the lawsuit was obtained Wednesday by The Associated Press.
It generally echoes a criminal investigation's findings - that Schuler was drunk, high on marijuana, and drove the wrong way for more than a mile on the Taconic Parkway north of New York City. It says she ignored signs and other motorists' warnings.
The collision with the Bastardis' SUV killed Schuler, her 2-year-old daughter, three young nieces, the Bastardis and their friend Daniel Longo, 74. Schuler's 5-year-old son, Bryan, survived.
The lawsuit claims that before they died, Michael Bastardi, 81, and Guy Bastardi, 49, a father and son from Yonkers, suffered "terror, mental anguish, and serious personal injuries" that caused them pain and suffering.
The crash - and the mystery of how Schuler could race against highway traffic with a cargo of frightened children - intrigued the nation and was featured on such TV shows as Oprah Winfrey's and Larry King's.
Michael Bastardi Jr., son and brother of the victims, said Wednesday night he hopes the lawsuit "will help bring out some of the answers we don't know about what happened that weekend before the crash. ... For a woman to do this with five kids in the car just doesn't add up."
Schuler and her husband, Daniel, had spent the weekend at an upstate campground and headed home to West Babylon in separate vehicles.
Daniel Schuler has refused to accept the autopsy conclusion that his wife had been drinking heavily and smoking marijuana. He has funded further studies that are still pending.
Calls to his attorney, David Smith, and to Hance's lawyer, James McCrorie, were not immediately returned. Hance lives in Floral Park.
The lawsuit does not specify an amount sought for the Bastardis' survivors, claiming only "pecuniary loss, funeral and burial expenses and other items of damage."
The civil lawsuit will be the first court action in the case. No criminal charges were filed because Diane Schuler was responsible for the crash "and the charges died with her," a prosecutor said.
Michael Archer, an investigator for the Longo family, said the family had not decided whether to sue. He said it was "in poor taste to sue Warren Hance at this time of year."