Dawn Brancheau, 40, died on February 24 when the whale named Tilikum grabbed her by ponytail and thrashed her around after a show. The whale has also been involved in two other deaths, one of a trainer at a Canadian park and another of a man who snuck past security and was found draped over the whale's body at SeaWorld.
Jon Mills, an attorney for Brancheau's family members, said in court that their right to privacy outweighs the public's right to view the video captured by SeaWorld cameras. At a hearing that lasted less than hour, he asked the judge to permanently stop the video from being released.
"There is no constitutional right to voyeurism and there is a constitutional right to privacy," Mills said.
Circuit Judge Lawrence Kirkwood did not immediately rule on the request for the permanent injunction. He had issued a temporary injunction last week to prevent the release of the video, which was turned over to law enforcement.
Unless Kirkwood intervenes, the material will become public under Florida law once the Orange County Sheriff's Office concludes its investigation.
Rachel Fugate, an attorney representing news organisations, said she didn't object to an extension of the injunction so all sides could reach a resolution.
She said there were precedents in recent Florida history that allowed news organisations to view images but not make copies for public dissemination. Members of the public, for example, were allowed to view photos of the mutilated bodies of five college students slain in Gainesville in 1990, but not copy them.
Grieving relatives have succeeded in keeping such images from being made public in other cases - Dale Earnhardt's widow successfully fought in Florida to prevent the release of autopsy photos of the race car driver, who died in a 2001 crash.
