If the marriage between a duke and duchess has been dissolved the former wife is no longer a peeress.
However she is allowed to keep the title as a duke’s wife but she has to put her forename in front.
For example Margaret, Duchess of Stepney.
If she remarries then she loses this right and reverts to her own name or her new husband’s name or title.
So if Margaret, Duchess of Stepney married Mr. Smith she would become Mrs. Margaret Smith.
A letter written to the former wife of a duke would start “Dear Duchess” and you would end it with “Yours sincerely”.
However on the envelope you would write “Margaret, Dutchess of Stepney”.
If talking to her you would refer to her as Duchess. For example, “Good morning Duchess”.
An invitation to lunch would be addressed to Margaret, Duchess of Stepney
If you were talking about the former wife of a duke you would refer to her as the Duchess of Stepney.
The place card at the table and any legal documents would refer to her as Margaret, Duchess of Stepney.