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From Tennessee Marriages 1801-1825:
Elizabeth Hooker married John Mills on 28 November 1815. The same source lists Elizabeth Hooker Mills' marriage to Matthew Hancock 13 March 1819. There is a pay voucher in the National Archives for Elizabeth's father, Benjamin Hooker, for his sevice in the War of 1812. The Battle of New Orleans was the last engagement of the war and was fought on 8 January 1815. The Treaty of Ghent had been signed 15 days before the Battle. This battle might have been prevented had cell phones already been invented. The point being that it is unlikely that Elizabeth's first husband, John Mills, was killed in that engagement. Benjamin returned along with his son and Elizabeth's brother, Joshua Freeman Hooker.
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1820 U.S. Census, Harrison County, Indiana
HEAD OF FAMILY

JOHN HANCOCK, 51; 9 year-old Judge; 14 year-old Benjamin; 1 male 16-18; 2 males 16-26 (Martin, 18 or 19); 2 females 16 to 26 (Jane, 20; Sarah, 18; Kathy, 16); wife, Jane Skeen Hancock, 49

SAMUEL HANCOCK, 24; 1 male to 10; 1 female to 10; wife, Francis Ann Avery, 26

MATHEW HANCOCK, 22; Baby Benjamin Hooker Hancock b. 12 Jan 1820; wife, Elizabeth Hooker, 18

JOHN HANCOCK, JR., 21; 1 male to 10; wife, Martha B. King, 21

PETER HANCOCK, 45 & c.; free man of color
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From Arvil Hancock:
John Hancock sold his plantation on the Cumberland River in 1819, freed his slaves, and moved his family north to Harrison County, Indiana

Matthew and Elizabeth were part of the migration to Harrison County. Matthew died 25 March 1848. Elizabeth died 09 November 1873. They are buried at Hancock Chapel Cemetery in Hancock Chapel, Harrison County, Indiana.