"Anny" is mentioned as the oldest daughter in Cornelius' will. There is an Anna Bodine who married a James Terneure. Their children were Catherine (b. 1814, Cayuga Co., NY) and Henry (b. 1827 in Cayuga).
She must have died before the lawsuit mentioned in her sister Catherine Bodine's notes. That was June 4, 1897. Ann does not seem to be mentioned in that lawsuit. It would look like she married a Robinson from the info in that lawsuit.
From Ronny Bodine:
In the will of her father she is called "my oldest daughter Anny Bodine." James and Ann Terneur were buried in Owasco Rural Cemetery, Skaneateles, Onondaga County. Their grave markers read: Ann Bodine Terneur died Sept. 24, 1871, ae. 80-2-27 (=27 June 1791), w/o James; James Terneur died Feb. 5, 1862, ae. 78-7-10 (=26 Oct 1783).
From New York federal Census Records:
1850 Owasco, Cayuga County: James Tewure 68 NY miller, Ann 58 PA, Henry 23 NY miller, Hannah Bodine 78 PA, Catharine Bodine 36 NY.
1860 Owasco, Cayuga County: James Turner 76 NY farmer, Ann 69 PA housewife.
1870 Owasco, Cayuga County: Ann Ternure 79 PA keeping house, Catharine Bodine 57 NY.