The Princess of Wales has “inner strength, the support of her husband and her extraordinary family, so she can focus on what’s important,” a former spokeswoman for Queen Elizabeth tells PEOPLE

After weeks of speculation online regarding her health and whereabouts, Kate Middleton revealed in a personal video message on Friday that she was undergoing treatment for cancer.

“She has the inner strength, the support of her husband and her extraordinary family, so she can focus on what’s important, which is her getting back to strength,” Ailsa Anderson, a former spokeswoman for the late Queen Elizabeth, tells PEOPLE exclusively in this week’s cover story.

In her self-written speech announcing her cancer news, Princess Kate, 42, said having Prince William, 41, by her side “is a great source of comfort and reassurance.” Meanwhile, their three children — Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5 — were a key part in the timing of her message.

“It has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be okay,” she said. “As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits.”

The family of five will spend the next weeks together privately while the children are on a school break, missing the tradition of attending Easter church service at St. George’s Chapel at Windsor Castle with members of the royal family this weekend.

Once Prince George, Princess Charlotte and Prince Louis return to the classroom, Prince William is expected to resume public duties. “The Prince will continue to balance supporting his wife and family and maintaining his official duties as he has done since the start of the year,” a Kensington Palace spokesperson said.

Meanwhile, Princess Kate will largely remain out of the public eye during her treatment, although she may join in events when she feels able. “The Princess will return to official duties when she is cleared to do so by her medical team. She is in good spirits and is focused on making a full recovery,” a palace spokesperson said on Friday.

With King Charles, 75, also largely out of the public eye while he receives treatment for cancer as well, other members of the royal family will continue to step up to represent the monarchy. Queen Camilla, 76, has maintained a busy schedule since her husband’s health news was revealed, while Princess Anne, Prince Edward and Sophie, the Duchess of Edinburgh also continue their royal work.

Those closest to Kate say they have every hope that when she is ready, the Princess of Wales will return stronger than ever.

“[The royal family] is vulnerable at the moment, and there will be an even greater appreciation that they are human beings with frailties like the rest of us,” says a former palace aide. “They are so dedicated to their roles. I think you will find when Kate makes a full recovery, she will come back even more passionate.”

Catherine, Princess of Wales during the trophy ceremony for the Women’s Singles Final between Marketa Vondrousova of the Czech Republic (not pictured) and Ons Jabeur of Tunisia at The Wimbledon Lawn Tennis Championship at the All England Lawn and Tennis Club at Wimbledon on July