It would be the crown that makes the invites. I doubt President Trump would stoop to being in the “US Delegation”, which given the Obama and Biden hatred for the UK will likely be filled with radicals, freaks, cross dressers, and other noxious individuals.
So if President Trump is given an independent invitation, the barrel of monkeys in the delegation can be seated in the rear, and he will have front row seats.
This will make the Democrats so mad that they will desperately try to get President Trump subpoenaed or otherwise held up, so that he can’t attend.
And the Palace is allowing individual countries to choose the members of their delegations.