And how are we to know? The Kents do not discuss their private lives with the public. On the official website, the Duke's biography states that he and his wife live at Wren House Kensington Palace, and in Oxfordshire.
The Duchess of Kent, born 22 February 1933, age 88, is the only daughter and fourth child of Sir William Arthington Worsley, 4th Baronet, and his wife, Joyce Morgan Brunner. Joyce Morgan Brunner was the daughter of of Sir John Brunner, 2nd Baronet, and granddaughter of Sir John Brunner, 1st Baronet, the founder of Brunner Mond, which later became Imperial Chemical Industries, or ICI.
Katharine's brothers are Marcus Worsley, Oliver Worsley, and John Worsley. Marcus died in 2012. Oliver died in 2010. She visited her brothers and they visited her---but this is all private information so we don't know how close they were. And, some of her brothers' children served as attendants during her wedding to the Duke.
She has not always enjoyed the best of health, and has retired from public duties. She has spent retirement from public life as a music teacher. She was teaching music in 2018, but not much has been said about her of late since she is a private person, known as Mrs. Kent to students.
https://en.wikipedia.org/wiki/Katharine,_Duchess_of_Kent