Inside Kate Middleton and Prince William's New Life in Windsor as a 'Modern Royal Family'

This fall has been a season of change for Prince William and Kate Middleton.

The new Prince and Princess of Wales, both 40, have gracefully navigated a pivot from personal grieving and global pomp following the death of William's grandmother Queen Elizabeth on Sept 8. into new landscapes at work and at home. At the end of the summer, the royal couple relocated with their three children — Prince George, 9, Princess Charlotte, 7, and Prince Louis, 4 — from London's Kensington Palace to Adelaide Cottage, a modest (by royal standards) four-bedroom home in Windsor's Home Park, the private 5,000 acres surrounding Windsor Castle.

The children are settling into a new school, Lambrook, where they began classes on the day the Queen died. A source close to the family acknowledges it has been a stressful time, especially for Princess Kate.

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"Things were very tense that week; it was not exactly the settling-in period they had hoped for," the source tells PEOPLE in this week's cover story.

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JONATHAN BRADY/POOL/AFP via Getty Prince George, Kate Middleton, Prince Louis, Prince William and Princess Charlotte

But the couple, following the lead of William's father King Charles III and Queen Camilla, are intent on showcasing stability and unity. As if to prove the point, Buckingham Palace released a poignant portrait on Oct. 1 of the foursome.

"That was a very important image of what the modern monarchy and reign of King Charles will look like," says Katie Nicholl, author of The New Royals: Queen Elizabeth's Legacy and the Future of the Crown. "They represent the future House of Windsor."

Chris Jackson/Getty Queen Camilla, King Charles, Prince William and Kate Middleton

As William and Kate embrace a heavier royal workload and the increased visibility that comes with it, they look forward to providing continued stability for their children at their new home in Windsor. In Windsor, the family relishes the open parkland and countryside where Prince George, Princess Charlotte and Prince Louis can freely play.

"They love that the kids can go out on their bikes and cycle around the estate, and they are all really excited to meet everyone," says a friend. "It's a real little community."

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For the first time, nanny Maria Turrion Borrallo is living separately from the family. Princess Kate wants her children to have as normal an upbringing as possible under their unique circumstances and is so far bucking royal tradition by keeping George at home rather than boarding school.

With Lambrook a 15-minute drive from home, Prince William and Kate try to do the school drop-off and pickup most days. And although insiders say they will eventually live in the 1,000-year-old Windsor Castle itself, for now cottage life is much like it is at their beloved country retreat, Amner Hall in Norfolk, where the kids and their friends are in and out of the swimming pool. George will flop onto the sofa beside his father, while Charlotte makes a beeline for familiar guests.

Theirs is a life of a "modern royal family doing normal things," as one close family friend puts it.

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Karwai Tang/WireImage Prince George, Prince Louis and Princess Charlotte at Trooping the Colour on June 2.

Whatever awaits them — and the monarchy — the royal couple will face it together.

It's all what Queen Elizabeth, whom William and Kate affectionately called "Grannie," would have wished, adds Majesty magazine's Joe Little: "She would expect them to carry on with a stiff upper lip and do so with grace."