Responses
Obviously, Alphonse and Chloe would be the next leaders. The crown prince is the emperor's only son, either a relative (the brother of the emperor for example) takes the throne or Alphone as he's a Duke. Dukes have always been a part of the royal family, as every prince who isn't the crown prince would become Dukes and next in line should something happen to the royal family. I'm unsure how close is Duke of Vanderberg to the Royal Family, but as they're Dukes they must be still of royal lineage.
This is my theory given we have never seen any relative to the royal family at all.
I feel like the Crown Prince will not repent. In the year future, he'll probably do something over the top and lose the position of heir. Now i'm wondering, who will be the heir to the throne?