Catherine isn't part of her official title because she wasn't a Princesses before her marriage. It has nothing to do with marriage or divorce. Her official title is: Her Royal Highness (HRH) The Duchess of Cambridge, Countess of Strathearn and Lady Carrickfergus. As a Prince before marriage, William is His Royal Highness Prince William Arthur Philip Louis, Duke of Cambridge, Earl of Strathearn along with additional titles.
While Diana was often referred to as Princess Diana, it was never her title before or after her marriage to Prince Charles. Prior to her marriage, she was Lady Diana Frances Spencer. While married, she was Her Royal Highness The Princess of Wales. Since divorce among the British royalty was so uncommon, Diana's post marriage title was part of her divorce settlement. She agreed to Diana, Princess of Wales giving up Her Royal Highness (HRH). There were some reports that Diana gave up the HRH for a larger financial settlement but those could be rumors. Queen Elizabeth offered to reinstate Diana's HRH status after her death but Diana's brother, Earl Spencer, refused to accept it. Many people think once King, William will reinstate his mother's status to HRH.
Sarah Ferguson accepted a similar arrangement (without much of a financial settlement) through her divorce agreement and went from HRH The Duchess of York to Sarah, Duchess of York. Without her children, Sarah and a commoner who brough t disgrace to the Royal Family it is most likely Sarah won't have received any title. However, as the mother of 5th and 6th in the line of succession, it was determine she would keep Duchess of York. This new practice of adding the woman's name before a title was adapted to recent divorces among the British Royal Family. Diana, Princess of Wales and Sarah, Duchess of York may have set a precedent for future royal divorces but that remains to be seen. Hopefully, the newly married and yet-to-be married young royals learned from the mistakes made by HRH Prince Charles of Wales and Prince Andrew (HRH The Duke of York).
Another example is Princess Michael of Kent. Baroness Marie Christine married Prince Michael of Kent. As the third child of George V's fourth son, a minor royal, he wasn't given any additional titles upon his marriage. They are the HRH(s) Prince and Princess Michael of Kent. They have no royal duties except to represent the British Royal Family at the marriage of minor royals worldwide.
I re-confirmed my answer, While the Palace has been pushing Kate to be referred as HRH The Duchess of Cambridge, she is also HRH Princess William. She is not HRH Princess Catherine.