The coronation of King Charles III is less than 100 days away — and he reportedly wants Prince Harry to be there.

Though the royal family has made no statement following the release of Harry’s bombshell memoir Spare, a source close to the royal household tells PEOPLE in this week’s cover story that the new British monarch wants his younger son to attend the May 6 ceremony at Westminster Abbey.

“It is such a momentous occasion for Charles, and he would want his son to be at the coronation to witness it. He would like to have Harry back in the family,” the source says. “If they don’t sort it out, it will always be part of the King’s reign and how he has left his family disjointed. He has had a reputation as a distant parent, and it would be awful for him for that to continue.”

Royal historian Robert Lacey tells PEOPLE, “Quite apart from [Charles’] paternal hope to reunite with his son, one of the jobs of the royal family is showing how to cope with the problems we all have in a human and thoughtful way. What will be a success for the family in the future is not reconciliation necessarily, but mutual acceptance of different ideas and priorities.”

Like King Charles and Queen Camilla, Prince William and Kate Middleton have also stayed silent on Spare.

“It is almost insulting to ask, ‘When are they going to kiss and make up?’ ” Lacey says of the strain that separates Prince Harry and Meghan Markle from some other members of the royal family.

“There have been some very grave disagreements between them. But the Platinum Jubilee [in June 2022] and the funerals of the Queen and Prince Philip did demonstrate that they could put personal enmity aside for the sake of the bigger cause,” he points out. “And that is what the coronation will be all about.”

According to a palace insider, Harry and Meghan will be invited to the coronation; however, a source close to the Sussexes says that an invitation has yet to be extended, and there has been no movement toward reconciliation.

Prince Harry’s initial position on the matter also hasn’t changed, the source says. When previously asked whether he would attend the coronation, he told ITV’s Tom Bradby last month, “There’s a lot that can happen between now and then. But, you know, the door is always open. The ball is in their court. There’s a lot to be discussed, and I really hope that they are willing to sit down and talk about it.”

Can’t get enough of PEOPLE‘s Royals coverage? Sign up for our free Royals newsletter to get the latest updates on Kate Middleton, Meghan Markle and more!

The way things stand now, there is still a long way to go. “The problem is that [the Sussexes] want a capitulation and apology by the palace, but when ‘recollections vary,’ that’s quite difficult,” adds the close source.

Fraught family relationships are a major concern, but the future of the monarchy is the ultimate priority of the royal family — and the pressure is on to modernize amid a rising tide of anti-royal sentiment.

Whether or not the Sussexes will be seen at the coronation ceremony, royal biographer Sally Bedell Smith says, “The monarchy is bigger than a family argument.”