Infanta Elena went as the representative of the King. Zarzuela said months ago that while Infanta Elena is not member of the Royal Family, she could represent her brother on special occasions.
Also King Juan Carlos sisters often represented him in events related to royalty or nobility, although they were never part of the Royal Family . They do not represent the Royal Family, but represent the House of Borbon.
The funeral of the Duchess was not an official or state funeral, so the presence of King Felipe and Queen Letizia, in this massive televised funeral in Sevilla, was not appropriate. King Felipe had his own acts in Madrid today.
King Juan Carlos or Queen Sofia who maintained a friendship with the Duchess for decades had been the appropriate representatives. But Queen Sofia is on a private visit in Athens since last week, last night attended the opening of an exhibition of El Greco and a conference today. And it is not known where King Juan Carlos is.
Probably in the next days the family will organize a mass in Madrid, and it is easier than a member of the Royal Family goes.