Given that I'm American and given that I think the coronation is a big celebration that is costly and mostly something that could be a place a crown on his head and "Tada you're King" now on to business, I don't think whose invited or not - especially children - should cause an such an uproar.
To be fair - I don't think the US Presidential inauguration should be as elaborate as it is either. It should be "sworn in" off to work event. Not the day or 2 day event.
Right now, I doubt Archie and Lilibeth really care about the coronation. Unless the press and adults cry foul, no fair, "you're insulted. You should be insulted for the rest of your lives" stuff. Children - young/teens - are easily bored. I would think by 8:15am before all the real ceremony begins they want to go to their rooms and play or talk to friends.
Really we don't know Charles' relationship with his grandchildren. Maybe he FaceTime's them more than the live time with his grandchildren in England. If he does FaceTime or zoom or whatever, Archie and Lilibeth would get more one on one dedicated time, because he would be solely focused on them during that time.
As for Camilla's grandchildren