Huh? I don't understand this comment, I thought we had put this issue to bed?
We have established by the Duke of York's site on Buckingham Palace's site that the title is HRH the Duke of York. He ceased to be known as HRH The Prince Andrew upon his marriage and his being created The Duke of York. A future wife would be HRH The Duchess of York, not HRH The Princess Andrew, Duchess of York. There is no such title.
The Royal Family > HRH The Duke of York > Background
This is standard in the Royal Family. When a higher title is created, the former title ceases to be used. This is not only the case for the Duke of York, but for all members of the Royal Family:
The Royal Family > HRH The Princess Royal > Background
Edited to add one more section illustrating the same point:
The Royal Family > HRH The Countess of Wessex > Marriage and family
I hope that's definitive enough. For the avoidance of doubt, it should be noted that this website is not a private site of the British Royal Family, it is an official government website as evidenced by the .gov in the web address.
Sarah, Duchess of York is correctly addressed as 'Duchess'. I have not been able to work out if this is the correct style for every divorced Duchess or a style granted her as an exceptional case by direct wish of the Queen.