"My assumption would be that someone like Lisa Marie," herself a second-generation celebrity familiar with Hollywood excess, "would say, 'It's better for me to be there with my daughter, rather than letting her go out by herself,'" Szish said.
But Pleshette Murphy said there are other ways to keep a watchful eye over teens.
"Kids today are exposed to a lot of things that we were not exposed to as kids," she said. "It's very hard for parents to negotiate a time in their kids' life which may be hard for them. But as close as they may have been to their child, this is none of their business."
Hands-off advice to kids may be better, Pleshette Murphy said.
"When they're in a relationship, they can give advice and hope that they [the children] do what's good for them, and you have to let go," she said. "That doesn't mean by holding their hair back and encouraging them -- just helping them make the right choices."
ABC News' Michael S. James and Kate Klonick contributed to this report.