She married 16 November 1761, at Easton, Suffolk, Arthur Chichester, 5th Earl and later 1st Marquess of Donegall, son of Hon. John Chichester and Elizabeth Newdegate, and nephew and heir of Arthur Chichester, 4th Earl of Donegall. Lady Anne was only ever known as the Countess of Donegall, as she died before her husband was created Marquess on 4 July 1791.
They had seven children, 3 sons, and 4 daughters but only the following 2 sons survived until adulthood;
George Augustus Chichester, born 14 August 1769, who succeeded his father as 6th Earl and 2nd Marquess of Donegall;
Lord Spencer Stanley Chichester, born 20 April 1775, died at Paris 22 or 23 February 1819
Lady Anne died at Bath on 11 November 1780 after a long illness, and was buried on 22 November 1780 at St Michael's, Lichfield.
Cokayne, George Edward, The Complete Peerage of England, Scotland, Ireland, Great Britian and the United Kingdom, 2nd ed. vol. 4, revised and much enlarged by Vicary Gibbs, assisted by H. Arthur Doubleday, London: The St Catherine Press, 1916. Electronic edition by ABC Publications, London, 2003.
Cokayne, George Edward, The Complete Peerage: or a history of the House of Lords and all its members from the earliest times, 2nd ed., vol. 6, revised and edited by Hon. Vicary Gibbs, H.A. Doubleday, Duncan Warrand & Lord Howard de Walden. London: St Catherine Press, 1926. Electronic edition by ABC Publications, London, 2003.
Lodge, Edmund, The Peerage of the British Empire as at present existing, London : Saunders and Otley, 1832. Digitised by Google Books.
Burke's PEERAGE (1913), p. 631
A source unknown calls Lady Anne Hamilton's mother Elizabeth Spencer, one of the two daughters and co-heiresses of Edward Spencer of Rendlesham, Suffolk, but Cokayne in two different volumes (see above) gives her name as Anne.