The Duchess was named Anne Horton, sometimes spelled Houghton, and they produced no children. Her Wikipedia article is here. Walpole wrote of, "the Duke of Grafton's Mrs. Houghton, the Duke of Dorset's Mrs. Houghton, everyone's Mrs. Houghton."
Grand Ladies
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ca. 1555 Caterina de' Medici by ? (Galleria degli Uffizi - Firenze, Toscana, Italy)
1775 Marie Antoinette by Jean Baptiste Andre Gautier d'Agoty (Châteaux de Versailles et de Trianon - Versailles, Île-de-France France)
1783-1785 The Duke and Duchess of Cumberland detail by Thomas Gainsborough (Royal Collection)
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