I find this tabloid-fed story about who will be visiting Invictus rather bizarre. The prince has broken relations with most of his family and he has betrayed their trust several times over during an extended period by selling out private details of them for financial gain. Grave accusations were made. As far as we know no steps have been taken to work on some kind of reconciliation. If there were to be any steps made in that direction it will most effectively be done in private. Not at an event with I don't know how many photo cameras there.
The absence of a private meeting between the King and his son indicates however that the time is not ripe yet for such a reconsiliation, and who knows if it ever can. I agree with posters that had the King trusted his son enough to meet him, a private meeting would probably have taken place.
In addition I fail to see why other relatives needed to be at this event at all, even if the relationship had been well. Members of the RF have lots of unique events each year, nearly none of those events will be attended by other royals. And if family support is so vital, would his wife, the Duchess of Sussex, not be the first and foremost candidate we could have expected to attend? She has stayed in California.
And finally, just imagine the King of the PoW going there, while the whole world & gathered press knows that the relationship between them and the Duke is frosty. It would have turned the event into a circus, which is the last thing anybody needs. It would have overshadowed the whole event. The tabloids would have been happy for sure, but the whole purpose of the gathering would be forgotten.