Not correct Rory! The children of the Sovereign are all styled with the definite article e.g HRH The Prince Edward, HRH The Princess Margaret, Countess of Snowdon. The confusion arises when the children of the Sovereign are granted honorific titles or peerages e.g The Prince Of Wales, The Princess Royal. The Duke of York etc. The first two of these examples are only accorded to the children of the Sovereign. Therefore, officially, The Prince of Wales is styled in this way or as The Prince Charles but not coupled together. Similarly with The Princess Anne.
The definite article is accorded to the remaining children of the Sovereign e.g. HRH The Prince Andrew, Duke of York though often in common usage reduced to HRH The Duke of York. However, the definite article accords the status of a child of a Sovereign whereas the grandchild of a Sovereign has no definite article and is styled either HRH Prince Edward, Duke of Kent or less formally, HRH The Duke of Kent, the definite article here belonging to the peerage rather than the individual.