Prince William Is Coping 'Remarkably Well' amid Kate Middleton's Surgery and King Charles' Cancer News

The Prince of Wales is taking a few days off with his wife Princess Kate, who is "progressing well" after abdominal surgery, and their children

Duty is calling for Prince William: duty to his immediate family and care for his wife Kate Middleton, who’s recovering from her abdominal surgery as well as duty to the monarchy and his father, King Charles, who suffered his own health setback when doctors discovered cancer.

Those very different demands have come into focus as the Prince of Wales, 41, starts a week off of royal outings to look after Princess Kate, 42, and their three children — Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5. As he does, there are ongoing discussions about what, if anything, he should do in terms of stepping in for his father, whose treatment for an as-yet-unnamed cancer continues.

On Feb. 7, when Prince William returned briefly to public duties that had been postponed due to his wife’s illness, he revealed little of the ongoing dual heartache as he, instead, showed deep interest in those he was honoring for their public service. Susan Taylor, who received an MBE for her work in rugby league (a sport Princess Kate is a patron of), told PEOPLE, "It is a difficult time for him, but it wasn’t spoken about. With all the royals it is stiff upper lip and duty as normal, isn’t it?"

Adds Ellen Convery, former soccer pro: "I sent my best wishes to the King and obviously to Kate, the Princess of Wales as well. He was lovely. He really appreciated it. I just wanted to send my best wishes."

Later that night, the prince thanked the public for the outpouring of support they’d given the family in recent weeks at a charity gala for London's Air Ambulance.

A friend told PEOPLE of Prince William's return to public life, "He is coping remarkably well considering his wife had surgery and he only found out his father’s news recently.”

Princess Kate, whom Prince William told one award recipient had received great care from two “amazing and kind” nurses, "continues to progress well” Kensington Palace officials tell PEOPLE.

A clear indication of her improving health came when she was able to travel to Anmer Hall in Norfolk, about 140 miles from Windsor, late last week for their children's half-term vacation from school.

For the Princess of Wales, the break will be a welcome change of scene. She enjoys living at Adelaide Cottage in Windsor, but Anmer Hall is a place of many happy memories of living there when their children were very young, including during much of the COVID lockdowns. They spent their Christmas break there before Kate’s diagnosis, joining local friends and families for outings, as well as enjoying the holiday festivities with the royal family.

Being in Norfolk also enables Prince William to be close to King Charles, 75, during the time his father is based there when not receiving treatment for his cancer. William visited his wife many of the 13 days she was in the hospital last month, and he will do the same during the time he and King Charles are near neighbors in Norfolk this week and when he can at Windsor, PEOPLE understands.

King Charles, who was pictured walking to and from church at Sandringham with Queen Camilla on Sunday, is keen to be seen as much as possible during his cancer treatment.

While the separate staff at Buckingham Palace and Kensington Palace respectively are in “constant dialogue," there hasn’t been anything specific that William has been asked to do on behalf of his father. Last week, a source who knows King Charles told PEOPLE that he wouldn’t burden his son unnecessarily.

“He wouldn’t want to put that pressure on William,” a source close to the royal household told PEOPLE. “He has always wanted to save his children from having that pressure too early and that will remain. Particularly as William has other priorities [with Kate].”

After his children's school break, Prince William is expected to resume a fuller diary of activities as well as take up the reigns of the school drop-offs and pick-ups.

Prince William will be seen "more than we have done in the last few weeks,” a source adds, as he tackles outings covering the range of his interests. That would be a sure, and positive, sign that Princess Kate is doing well enough to enable him to do so.

He is likely to be at the Commonwealth Day service on March 11 while Queen Camilla, 76, will represent her husband. There is also a chance he will be at the biggest night for British film, the BAFTA ceremony, on Sunday, though his appearance will depend on the situation at home.

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At the end of the month, both William and Kate will have new executives running their offices. A new private secretary in the form of Ian Patrick is coming for the Prince of Wales. A former diplomat, Patrick worked at the Foreign and Commonwealth Office in international peacekeeping in Bosnia and Herzegovnia. He is also a trustee of the charity Crohns and Colitis U.K.

The Princess of Wales' staff will be led by Lt. Col. Tom White, who was most recently the late Queen Elizabeth’s equerry. On the heels of those appointments will be a CEO-type appointment to head up the couple’s joint teams.

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