Her article in thepeerage.com is here. She was Anne Villiers' daughter. Philip Mould's excellent article about this portrait dates it to about 1714.
From Philip Mould; spots removed throughout image and the edges cleaned up with Photoshop by gogm.
Keywords: 1714, Dagar, Bentinck family, Pierrepont family, Duchess, British, long straight coiffure, scoop décolletage, modesty piece, chemise, negligee