The former Fashion Police host candidly talks about parenting and keeping her mother's name alive

It has been nearly four years since Joan Rivers died — but her daughter, Melissa Rivers, says that her influence is still felt every day.

“I really notice my mom in my parenting,” says Melissa, 50, who is mom to 17-year-old son Cooper. “I’ll say something, and as soon as the words come out of my mouth, I’m like, ‘Wow. I sound just like my mom!'”

“And then I hear my father coming out, too!” she continues, referring to dad Edgar Rosenberg. “I was a big negotiator when I was a teenager, and my son tries that, too. Every time I say, ‘This is not my negotiation,’ I hear my father! He used to say that all the time!”

“One of my friends told me the other day that I shouldn’t negotiate with terrorists,” she says, laughing, “and I said, ‘Especially when you’re the hostage!'”

“I think I’m a fair mom,” Rivers says. “I’m very clear on what the rules are. I’m very clear that these are the parameters in which you may operate on. If you stay there, you’re good. If you don’t, your life will crash down around you. I always remind Cooper, ‘I can make your life miserable. Please don’t tempt me.'”

92nd Street Y Presents: An Evening With Joan And Melissa Rivers
Credit: Noam Galai/WireImage

Rivers tells PEOPLE that she sees Cooper as a way to keep her mother’s legacy alive.

“The best legacy that I can give my mother — that everyone can give their parent — is to raise a good and decent child,” she says. “One who gives back, and has a clear understanding of the understanding of not just being good, but doing good, as well. Cooper is my mom’s greatest legacy.”

“Cooper and I often talk about what is our family legacy,” Rivers says. “And I feel like our legacy is to live a life that you can be proud of on many levels. Giving your best professionally and personally. Giving back to others. Cooper and I always try to remember how fortunate we are, just by rite of birth. We can never lose sight of that. We’re not entitled to anything. We work for what we have. That’s how my mother lived.”

RELATED VIDEO: What Made Joan Rivers Such a Great Grandma?

PEOPLE caught up with Rivers at Runway to Hope, a charity fashion event that fights pediatric cancer. The event, organized in Orlando by lawyer and former CNN analyst Mark NeJame, has raised millions of dollars to fight the disease. Rivers co-hosted the show with Lisa Ling and Joey Fatone.

“My mother taught me this,” says Rivers. “When people ask me to do an event to help kids, the first questions are where and when. I can’t even begin to get my head around what it would be like to deal with cancer in your child, so if I can help other families who are going through this, I will.”

The event pairs celebrity guests with children who have fought cancer. The kids get their hair and makeup done, and walk a runway in clothes that have been donated by high-end brands.

So would Fashion Police host Joan Rivers have approved of the event? “Oh my God, yes.” says Rivers. “Obviously, my mother loved fashion, but she would have really loved to see it being used in this way, to make these kids feel good about themselves. This would have totally been her thing.”