Clinton also acknowledged that for Chelsea's boyfriends, "It was really intimidating to talk to her father. And, I guess, to me."
Clinton joined the panel from North Carolina, where she was campaigning before the state's primary Tuesday. She took questions from a largely-female audience in a high school auditorium here.
The mostly lighthearted discussion focused mainly on how Clinton had balanced work and family when Chelsea, now 28, was growing up. But it also produced a few revelations.
The former first lady said that when Chelsea was a little girl, the family would organize a group activity most Wednesday nights, like going to a movie or hitting tennis balls.
One family night involved a coconut, Clinton said.
"Chelsea said she had heard about coconuts, but had never seen one. So we went to a store and bought a coconut and took it home," Clinton recalled. "Bill and I, between us, had 50 years of education but we could not get the coconut open. We were throwing it on the driveway, we were beating it with a hammer. We were so embarrassed."
Clinton was gingerly asked by one of the panelists, family therapist Shannon Fox, on how she had guided her family through "difficult times" - a clear reference to her husband's affair with White House intern Monica Lewinsky that led to his impeachment in 1998.
"When you are in a difficult situation, oftentimes you just want to withdraw and just shut yourself out. When you have to do it in front of the world, that's different," Clinton said, adding that she had relied on her religious faith and her friends to help her through the crisis.
At least one question appeared to puzzle the New York senator. "You've seen, Senator Clinton, all these reports of young girls becoming very aggressive," Fox asked. "Do you think these girls are becoming more violent? Are we raising aggressive women?"
"I don't know about that," Clinton said, before saying she recalled seeing stories about teenage girls videotaping themselves bullying other girls.
"What kind of lessons are they getting at home that they are so desirous of seeing themselves on the Internet attacking a fellow student?" Clinton asked.
