Well, the old Duke of Gloucester was already in a very bad way even before Prince William died; I'm pretty sure that if he'd been King, some sort of at least semiformal regency would have alreaady been in place. But I agree that having a child die, especially as a young adult, must be devastating for a parent. Even though Princess Alice lived for several more decades, all reports are that she was never quite the same again after her son's death.