The parents say their 10-year-old son, who was at the show that day, has been traumatized.
CBS News correspondent Ben Tracy reported on "The Early Show" Friday that the family says Bobby Connell was right there and saw the 12,300 pound orca Tilikum attack and drown trainer Dawn Brancheau at SeaWorld's Shamu Stadium in February.
The Connell family even took a home video, just moments before the attack. Bobby can be seen looking on.
In the lawsuit filed this week, the family says Bobby "saw the look of horror and desperation on Dawn's face as she was swimming for her life," and, "Tilikum violently yank her down to the depth of the pool."
The family claims the boy now has nightmares, is often angry, and doesn't eat.
But CBS News Legal Analyst Trent Copeland says, "It doesn't matter that the boy was traumatized. It doesn't matter that he experiences severe emotional distress. Really, what the courts look to is whether there was a close family relationship between the person who observed the accident and the person who was injured."
More than 50 witness statements were collected after the attack and this is the only suit so far.
SeaWorld declined to comment on the specific case, but in a statement said, "We are in the process of a thorough review of our killer whale program right now and will make any changes that we feel will improve the safety of our staff and guests."
On Monday, the Occupational Safety and Health Administration, citing SeaWorld for three violations including "willful" disregard for safety because Tilikum had "known aggressive tendencies."
The whale was involved in two other deaths in the past 20 years. SeaWorld is appealing the government's findings and plans to fight the Connell family's suit.
On "The Early Show" Friday, Suzanne Connell told how her son, who also appeared on the broadcast, has been affected by the trainer's death. Bobby didn't speak on the show, because of the pending lawsuit.
"Since it happened, he -- at first it was the first week or so was very much shock," Suzanne said. "He had a hard time eating. He spent a lot of time alone. Crying a lot. Didn't want to talk about things. Didn't want to talk about that. You know, angry a lot. Nightmares. It was very difficult for the whole family, but he took it really hard."
She continued, "Today -- well, you know, it's been six months ago it happened on Tuesday, you know, and things don't seem to be getting any better. He's doing a little bit better, but then we had nightmares again last week. It just seems to not be going away at all."
"Early Show" co-anchor Erica Hill asked, "Did you realize at the time what you were seeing?"
Suzanne replied, "As soon as he pulled her in, I knew something was wrong. I screamed to the trainer. And then, basically, we kind of stood there in shock. You know, it just -- it wasn't real. It wasn't happening."
John Overchuck, the Connells attorney, said the family wants SeaWorld to accept responsibility.
He said, "They don't seem to understand there are consequences for their actions. It's been six months now. And SeaWorld has taken no responsibility for anything that happened that day. In fact, everyone who has criticized SeaWorld has come under their attack. So, we can start with just accept responsibility for this event and make sure it doesn't happen again."
Hill pointed out that "The Early Show" did contact SeaWorld.
"They told us they are not commenting on this specific case right now," Hill said. "They're reviewing the killer whale program."
She added, "When we asked (SeaWorld about this lawsuit), they brought up another claim, saying the Connell family had a different attorney who contacted SeaWorld on their behalf asking for $5,000 or threatening, if not, to go to Oprah with their story. What do you know about those claims?"
Overchuck replied, "I know that the Connells absolutely deny that that's true. And I also know that there's this phantom lawyer out there who is supposed to have said these mysterious things which somehow can be construed to make the Connells look bad. Now, one of the things we're going to do in this case is we're going to get to the truth. And I'm going to find out from SeaWorld who this person is, if he, in fact, exists, and if he exists, did he do what they're accusing the Connells of doing?"
Hill replied, "So, just to be clear, Mr. Overchuck, in this suit, you simply want to hear from SeaWorld some admittance. You're not necessarily looking for a financial payout here?"
Overchuck responded, "Well, the only way that a corporation can say I'm sorry is with the dollars that they earn every day."