"She was a young mother but she wasn't phoning it in and she was very involved," Jackie Style author Pamela Keogh says of the former First Lady

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Jackie Kennedy was well known for being a groundbreaking style icon – but the former First Lady was also a pioneer when it came to parenting.

Jackie Style author Pamela Keogh describes Jackie as being an “extremely hands-on, very involved” mother. “Especially for that class, for that gang,” Keogh adds of the rest of the Kennedy clan.

As mom to Caroline and John Jr., “Jackie was – there,” Keogh tells PEOPLE. “She was there playing with them and reading to them and painting with them – all kinds of stuff. She was a young mother but she wasn’t phoning it in and she was very involved that’s why her two children were beautifully raised.”

While the Kennedys’ beloved family nanny Maud Shaw was always on hand to give the children baths and late-night bottle feedings, “Jackie oversaw absolutely everything,” Keogh explains.

And though the Kennedy kids had every luxury at their disposal while living at the White House, it was important to Jackie that they remained “modest, humble and down-to-earth,” Keogh says. “They had to pick up their own clothing. She made sure that the Secret Service agents were not maids. The Secret Service agents could not fetch the children anything.”

The First Lady and her husband, President John F. Kennedy, “insisted on their children being respectful, acknowledging people and having good manners,” recalls Clint Hill, Jackie’s former Secret Service agent and the author of Mrs. Kennedy and Me. “But at the same time they wanted them to have a lot of fun and be happy.”

The First Lady did everything in her power to protect Caroline and John Jr. from the press, but she also made sure they engaged with the outside world and with other children, including but certainly not limited to their young Kennedy cousins.

“When they were at the White House there was a privilege involved there but still they weren’t isolated,” former Secret Service agent Tom Wells tells PEOPLE. “Ms. Shaw used to take them to the park to meet their friends. They went to other friends’ houses from time to time, and their friends would also come to the White House. They were engaged in a lot of activities.”

Jackie also wanted her children to be “independent,” says Keogh. “If they got themselves into a scrape they had to get themselves out of it.”

The president and the First Lady “never wanted us to pick the children up when they fell down or anything,” Hill recalls. “That was up to them to have to figure out how to get up.”

As the disciplinarian of the family, “Jackie ran a tight ship,” Keogh says. “She checked the homework and she made sure they were dressed properly. If John was acting up, she made him go stand in a corner. It wasn’t a tough house but there were expectations.”

But the First Lady was as playful as she was strict, and she loved to share her own passions with her children.

“She was fun. You can see the pictures,” Keogh adds. “She was running with the kids and playing with them.”

“She enjoyed things like trying to teach Caroline how to ride, things that she liked herself,” says Hill.

“Mrs. Kennedy taught Caroline how to water ski,” he adds. “She got in trouble because in 1962 in Italy she had Caroline on water skis with her, one pair of skis. Caroline was in front of her and there was no safety apparel at all.”

“Some of the British press were really up in arms. They said that she risked the safety of her daughter.”

But Jackie, ever-confident in her parenting skills, had the perfect response.

“I think she laughed.”