As Will Johnson stated in his first message, Anne and Elizabeth were the daughters of Edward Spencer of Rendlesham (PROB 11/615/135 ). See these abstracts from the National Archives:
Anne, the elder daughter, married the Duke of Hamilton:
Elizabeth, the younger daughter, married Sir James Dashwood. See The Derby Mercury, 22 Feb 1738, p. 4, col. 2, digital image in Newspapers.com:
"On Saturday Morning last Sir James Dashwood, of Northbroke in Oxfordshire, Bart. was marryed at St. George’s Chapel, Hyde-Park-Corner, to Miss Elizabeth Spencer, Daughter of the Lady Barker, of Suffolk, by her first Husband, - Spencer of Red-Lion-Square, Esq; and Sister to Her Grace the Dutchess of Hamilton, a very agreeable young lady of 70,000 l. Fortune."
Lady Barker, widow of Edward Spencer and mother of Anne and Elizabeth died in 1754. See The Derby Mercury, 29 Nov 1754, p. 2, col. 4, digital image in Newspapers.com:
"On Tuesday Night died, at Sproughton in Suffolk, (the Seat of Sir John Barker, Bart.) the Dowager Lady Barker, Relict of the late Sir William Barker, and Mother to her Grace the Dutchess Dowager of Hamilton, and to the Lady of Sir James Dashwood, Bart."
Anne Barker was buried 2 December 1754 at St. Gregory the Great, Rendlesham, Suffolk, according to a transcription of the National Burial Index available in Findmypast.
Anne Duchess of Hamilton married (2) Hon Richard Savage Nassau
and The Newcastle Courant, December 28, 1751, p. 1, col. 2, digital image in Newspapers.com
"On Monday last was married, at her Seat in Suffolk, by the Rev. Dr. Newton, Rector of Bow, and Lecturer of St. George Hanover-square, her Grace the Dutchess of Hamilton, to the Hon. Richard Savage Nassau, Esq., Brother to the Right Hon. the Earl of Rochfort, and Member of Parliament for Colchester."
She died 9 March 1771. See The Ipswich Journal, 16 March 1771, p. 2, col. 2, digital image in Newspapers.com:
"On Saturday died her Grace the Dutchess Dowager of Hamilton. Her Grace was relict and third wife of the Duke of Hamilton, grandfather of the present Duke. She was one of the daughters and coheiresses of – Spencer, Esq; near Ipswich, in Suffolk, and after his Grace’s death married the Right Hon. Richard Savage Nassau, brother to Lord Rochford, by whom she had two sons and a daughter.
By the death of the late Dutchess Dowager of Hamilton, a jointure of 2,000l. per annum descends to her eldest son, Lord Archibald Hamilton."
Ann Nassau was buried 17 March 1771 at All Saints, Easton, Suffolk per a transcription of the National Burial Index in Findmypast.
The National Burial Index states Elizabeth Dashwood was buried 28 April 1798 at St. Gregory the Great, Rendlesham, Suffolk, aged 80 years. Her will identifies her as the widow of Sir James Dashwood of Kirtlington Park, Oxford (dated 20 Dec 1796, proved 26 Apr 1798, PROB 11/1305/218, digital image in Ancestry).