Meet Eunice Kennedy Shriver's Grandkids, Who Are on a Mission to Carry Her Special Olympics Torch

It's a Thursday afternoon at Maria Shriver's Los Angeles home when, at her request, daughter Christina Schwarzenegger and niece Molly Shriver enter the frame of Maria's Zoom call. Maria is joined by her brother Tim Shriver Sr. to discuss their mother Eunice Kennedy Shriver's Special Olympics legacy ahead of her would-be 100th birthday on July 10, but as far as Maria is concerned, Molly and Christina should be the ones talking.

Molly had been "upstairs doing her laundry," says Maria, 65, who jokes that her niece "was shocked that she was not included in this call." That's because Molly is the chairwoman of the Special Olympics Founder's Council, a group of six Shriver cousins whose goal is to push for the more inclusive future their grandmother Eunice envisioned for people with disabilities even before her brother John F. Kennedy became president.

"My grandmother walked the walk and sprinted the sprint," Molly, 23, tells PEOPLE in this week's issue. "To show people the importance of something, you have to do it — and that came to her so organically."

Molly Shriver and Christina Schwarzenegger

The family says the "heart root" of Eunice's activism was her sister Rosemary Kennedy, who was born with intellectual challenges and underwent a disastrous lobotomy in 1941 that left her with the the mental capacity of a toddler and in need of a wheelchair. But Eunice saw possibilities in Rosemary where others saw limits.

"There was never anything that my grandmother didn't think she could do," says Christina.

Keystone-France/Gamma-Keystone via Getty Rosemary Kennedy and Eunice Shriver with Edward Moore in 1938

For Molly, who grew up 10 minutes from Eunice in Hyannis Port, Massachusetts, that meant suiting up for races.

"My grandma built this pool with a wheelchair ramp just so that Rosemary could get in, and then she would make me have a swimming competition against 80-year-old Aunt Rosemary," she says, laughing. "I don't know many people who know their great aunt. I was fortunate."

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Courtesy Special Olympics Clockwise: Christina Schwarzenegger, Molly Shriver, Tim "Timbo" Shriver Jr., Tommy Shriver, Natasha Hunt Lee, Kathleen Shriver

Along with Molly and Christina, 29, their cousins Tim "Timbo" Shriver Jr., 32, Kathleen Shriver, 27, Natasha Hunt Lee, 24, and Tommy Shriver, 21, have all pledged to carry Eunice's Special Olympics torch. As members of the inaugural Founder's Council, they'll volunteer at outreach events, play in and coach unified sports games, and raise awareness for their grandmother's cherished cause.

"It's really about continuing her tradition," Christina says of Eunice, who died at the age of 88 in 2009.

For more on the Shriver cousins and their work to honor grandmother Eunice Kennedy Shriver, pick up the latest issue of PEOPLE, on newsstands Friday, or subscribe here.

The extended Shriver clan in Hyannis Port, Massachusetts, in 2019

It's a legacy that began in 1962 at the family's Bethesda, Maryland home with Camp Shriver, a backyard summer sports camp for children with disabilities. By 1968 Eunice had turned her passion into the Special Olympics, which holds the World Games in a new city across the globe every two years. Through grassroots community support and national programs that encourage schools to have unified sports teams that include people with and without disabilities, Special Olympics now helps 5.5 million athletes in 190 countries realize their dreams — on and off the field.

"I have an enormous sense of pride for her and for everything that she's created, especially at the time that she did so," says Molly, who notes that Eunice grew up in a family "that put a lot of attention on the men."

Courtesy Special Olympics, Inc. Eunice Shriver teaching kids to swim during Camp Shriver's early days in the 1960s

Now the Shriver cousins are following in their grandmother's footsteps as ambassadors for the organization.

"It was ingrained in us since the day we were born," says Christina, a producer and documentary filmmaker who helps Special Olympics with marketing ideas. "I was 6 or 7, and she'd be like, 'Are you starting a Special Olympics chapter? Get me a list of 50 people — you're going to create it by the end of this week.' And I'd be like, 'Grandma, I don't even have a phone.' But it was this mentality of 'figure out what the problem is, and come up with a solution.' "

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The cousins got the best training possible, having spent summers with Eunice at the family's homes in Maryland and Cape Cod.

"Immediately upon arriving, there were five different athletes who you'd jump in the pool with or play sports with — it became a way of life," says Kathleen, a journalism grad student at Columbia University who develops social media campaigns with Special Olympics athletes.

They also learned from seeing Eunice wow crowds on the world stage. Timbo, a father of two (with wife Tamara) who cofounded the Spread the Word campaign, tells PEOPLE he was inspired by watching Eunice speak with President Bill Clinton at the 1995 Special Olympics World Games in New Haven, Connecticut, where thousands showed up for the festivities.

"I was 6, and I saw my grandmother giving this incredible speech," Timbo says. "I was totally captured by her and what she had done."

Kathleen Shriver, Eunice Shriver and Tommy Shriver

Tommy, a rising senior at Boston College, says the women in his family are "just as driven and passionate as my grandmother was."

That comes out in the cousins' active summers at the Cape together.

"Everyone shows up to dinner exhausted like a noodle," says Natasha, an NYU-educated singer-songwriter, "because we've done seven different sports in one day."

Adds Timbo: "We try to keep up our grandmother's competitive edge. We try to live that out in our family lives."

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Eunice Shriver (center), her husband Sargent Shriver (far right) and 16 of their 19 grandchildren celebrate her 85th birthday in 2006

Still, the cousins acknowledge they have big shoes to fill.

"Growing up in a family where your last name is recognizable, there's a lot of pressure to live up to that success, but the great thing about what we look up to is it's human-driven," says Molly, who has coached a Special Olympics Unified basketball team and is pursuing a career in criminal justice reform.

"It's not to be the most wealthy person on Wall Street or the president," she adds. "It's to be the most respectable human being you can."

To support the Special Olympics, go to jointherevolution.org, and to learn more about the organization, visit specialolympics.org.