This Ballard family intrude into my family history research at different times & I am still trying to unravel the links.
Have an Eliza Ballard Wheeler born 3 March 1805 at St Lukes Chelsea whose father was Willam Wheeler and mother was Esther Lewis.
Other as yet unrelated events include,
George Wheeler married Mary Ballard 4 Feb 1754 Hampshire
Francis Ballard Wheeler b 19 August 1810 at Sth Littleton married Ann Ellis
William Ballard Wheeler (b 7 October 1795 d 1843 Alderbury) married Abby unknown
Sarah Wheeler married John Ballard in Hampshire
Edith Louisa Ballard Wheeler b Sept 1904 Lambeth
There are other occurences of the Ballard name in Wheeler area.
Can you fit any of these into your research.