What’s Next for the Growing McCain Clan: Cindy’s Ultra-Private Daughter Bridget Is Her Neighbor Now!

Three years after the death of her husband — the late Sen. John McCain — and in the wake of the death of his 108-year-old mother, Cindy McCain is taking on the banner of family matriarch with pride, joking to PEOPLE in an interview for this week's issue that the rest of the family "should carry me on a sedan chair."

Cindy, 66, became the elder of the McCain clan after John's mom, Roberta, died in October.

Calling her mother-in-law an "amazing human being," Cindy notes that if only others understood more about the McCain family tree, which includes plenty of strong women.

"I wish they knew more about the other McCain women that were alive during my period but also the ones in the past," she tells PEOPLE. "There are strong pioneer women that were dedicated to service; amazing women, really, all of them. And I'm just grateful to be a part of all this."

Her new memoir, Stronger, out this Tuesday, details Cindy's four-decade relationship with John and how she has learned to live with, as she writes, "the heartbreak of loss."

In the wake of John's death in August 2018 from an aggressive form of brain cancer, Cindy tells PEOPLE she has been coming into her own and taking solace in time spent with her children — Jack, Jimmy, Meghan and Bridget — and a growing number of grandchildren.

Meghan, 36, welcomed an "adorable" daughter, Liberty Sage, with husband Ben Domenech in September.

• For more on Cindy McCain's life and to read an exclusive excerpt of her memoir, Stronger, subscribe to PEOPLE or pick up this week's issue, on newsstands now.

"She is just the sweetest thing ever," Cindy gushes, adding that Jack, 34, lives in Arizona with his wife, Renee, who serves in the U.S. Air Force, and their young son, Mac.

"So they're right now bicoastal ... He's now in the Navy Reserves," Cindy says. "Still flies but also works for American Airlines as a government relations guy. And he's doing great."

As a grandma, Cindy is the "baby whisperer," Meghan previously told PEOPLE: "Liberty is obsessed with her. I was like, maybe [it's] because my mom had four kids, but she was hypnotized by my mom."

"My mom knows every single answer to every baby question, it's crazy," Meghan said.

Thirty-two-year-old Jimmy, meanwhile, is expecting another baby with his wife, Holly, and studying as a graduate student at Trinity College in Ireland. "So little Luke [Jimmy and Holly's older son] will have a brother or sister coming up," Cindy says of the family.

And Bridget, the youngest and most private of her seven siblings — John has three children from his first marriage — is a college student studying speech and hearing at Arizona State University and she now lives close to her mom.

"Bridget is doing just great," says Cindy. "She's just a lovely human being and very funny and witty. And I'm just so grateful to have her as a neighbor now."

In fact, Bridget, 29, lives not far from Cindy's home in Phoenix: "I get to see her a little more," Cindy says.

She's seeing more of her children in general, she says: "I think they want to make sure I'm okay, and I'm doing just fine, but I appreciate seeing them. It's wonderful."

Bridget, who has almost entirely avoided the spotlight, made headlines in 2020 when she directed a tweet at former President Donald Trump over his long history of criticizing her dad.

"Even if you were invited to my dad's funeral, you would have only wanted to be there for the credit and not for any condolences," Bridget wrote, after Trump said he never liked McCain. "Unfortunately, you could not be counted on to be courteous, as you are a child in the most important role the world knows."

Though Cindy tells PEOPLE she was "stunned" that Bridget wrote something, due to Bridget being so private, she adds that she "could not have been more proud" of her daughter.

"I just thought, 'Whoa, it's in there.' She's so quiet most of the time, and she's so introspective, and then all of a sudden this came out and it was so beautifully written that I was very proud of her," Cindy says.

With her new memoir, Cindy is also reflecting on motherhood, including the unusual arrangement in which she and the children remain based in Arizona while John worked weekdays in Washington, D.C.

Raising all four kids with their distinct personalities, Cindy tells PEOPLE, included a fair share of "chaos" — though it helped to have an attentive partner.

"I'll admit: Chaos was part of it. I will say that at the times that I needed John, he never hesitated to pick up the phone, no matter what meeting he was in," Cindy says. "So if I had trouble, and I could put Jimmy or whoever it was on the phone, he'd help me out with that."

She continues: "Our parenting style was we co-parented — we did it together. We always consulted and made sure that we gave them the best values that we could."