Is Rothesay under the same conditions as Cornwall (eldest son of the monarch who is the heir), or would William still automatically receive that dukedom should Charles predecease The Queen?
My understanding it that yes it is.
Wikipedia tends to support my understanding:
An Act of the
Parliament of Scotland passed in 1469 governs the succession to most of these titles. It provides that "the first-born Prince of the King of Scots for ever" should hold the dukedom. If the first-born Prince dies before the King, the title is
not inherited by his heir – it is
only for the first-born son, like the
Duchy of Cornwall — nor is either inherited by the deceased duke's next brother,
unless that brother also becomes heir-apparent. Though the Act specified "King," eldest sons of Queens Regnant subsequently also held the dukedom. The interpretation of the word "Prince", however, does not include women. The eldest son of the British Sovereign, as Duke of Rothesay, had the right to vote in elections for
representative peers from 1707. (The 1707
Acts of Union between the Parliament of Scotland and
Parliament of England formally unified both kingdoms to create the
Kingdom of Great Britain). This right continued until 1963, when the
UK Parliament abolished the election of representative peers.
Duke of Rothesay - Wikipedia, the free encyclopedia
At the end of this entry it lists all the holders and George III isn't listed as a holder which again supports the idea that it is a title only held by the heir apparent to the throne who is also the eldest son of the monarch.