The oldest daughter of former senator John Edwards, Cate has followed in her late mother's footsteps as an advocate for women with cancer and recently joined the "Count Us, Know Us, Join Us" campaign, which recognizes those living with advanced breast cancer, their caregivers, supporters, friends and family members.
The 31-year-old, who wed longtime boyfriend Trevor Upham in 2011, says being by her mother's side during the six-year-long battle was "enlightening in a lot of ways, and being a part of that process with her was momentous for me."
"[My mother] taught me that it's OK to be down some days, but she generally had a really optimistic outlook," Edwards told PEOPLE at the London NYC Hotel on Thursday. "Her takeaway and immediate reaction to her diagnosis was, 'Hey, I don't know how long I have left, and I'm going to make sure that all of that time is lived with purpose and to make every day count.'"
The attorney and best-selling author left a lasting legacy for her three children, but perhaps the most precious one is a three-page letter she wrote for her oldest daughter.
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While continuing to juggle her advocacy work through her job as a civil-rights attorney, Edwards and her family have almost finished creating the grave marker for her mother.
"It's taken a long time because it was so important to our family to get it right," she says. "The idea is that it will resemble the optimism, hope, grace and strength that she lived with."
Even though she now lives in Washington, D.C., and her father and siblings live in Chapel Hill, N.C., Edwards remains close to her family.
"We all went through this together," she says. "My family is doing well. I'm seeing them regularly but not all the time. I was just in North Carolina last week, actually."
And Edwards says that her father, who also has a daughter, Quinn, 5, with his former mistress Rielle Hunter, is doing OK as a single dad to his younger children with Elizabeth – Emma, 15, and Jack, 13.
"I think it's tough, but he's really enjoying it," she says. "He spent the summer with the kids relaxing, but I think he's happy."