Individual Details

Jane is often seen with a death date of 1781 in Louisville, but I think that's very wrong. I believe, she married for a second time after 1796.

A message board post tell a very different story about Jane.
http://genforum.genealogy.com/archer/messages/2346.html
The article is about an Indian tradition of the Archer family, some of whom were believed taken prisoner in Cumberland Co PA, 4 Nov 1757 [Joseph Hunter was also from Cumberland].
The article has this to say about Joshua Archer, and does not tie him into the family:
Among those related to the family was Joshua Archer, a member of Capt. George Owens' Company at Ft. Jefferson, many of whom were said to have had Indian wives. He was probably in the same family as James Archer who claimed land on the South Fork of Ten Mile Creek near John Owens old trading post and David Owens' claim in 1772. Joshua Archer's name was often abbreviate in the court records as "Jos." so that he and Joseph Archer are sometimes indistinguishable. See "Virginia Land Grants in Pennsylvania" which is reprinted in The Pennsylvania Genealogist, Vol. II, 1967, pp. 126-127.
....Joshua Archer was with a party of explorers and surveyors "from the back part of Pennsylvania" with John Finley at Upper Blue Licks in 1773. See Fleming County Land Book B, p. 2594, deposition of James F. Moore, taken at Bush's tavern in Frankfort, Ky, 1804.
In Kentucky with David and George Owens, Joshua Archer claimed the land "lying on the south side of Salt River about three miles from Bullitt's Lick at the Buffalo Crossings to include his improvement about three or four hundred yards from the river." Like David Owens, he had abandoned his land claims at Hannastown, Pennsylvania and their land was sold at a sheriff's sale in 1785. See WPHQ, vol. 59, #2, p. 158.
After Ft. Jefferson was abandoned, Joshua Archer returned to Louisville with his father-in-law, Joseph Hunter. The name Joshua Archer appears often in the court records of Jefferson County, Kentucky--often abbreviated as "Jos." In the original drawing of lots in Louisville, Joshua Hunter drew lot #26 on the old plan. In 1784, he was sued by his brother-in-law, John Donne, for assault and battery. Also in that year, Joshua Archer and his wife were involved in a scandal with Richard Clark, a brother of Gen. George Rogers Clark.
Joshua had married his wife, Jane Hunter, at Ft. Jefferson and they had at least one child, Mary Posey Hunter, and perhaps more. Joshua Archer was captain of the Jefferson County Militia in 1787. He seems to have left the area by 1796, and his name thereafter appears in the records of Brown County, Ohio, associated with Joseph Hunter. Jane Archer re-married Jeffersonville tavern-keeper George Jones, who administered Joshua Archer's Kentucky estate.

Joshua was actually the son of Sampson Archer:
http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=brendablack&id=I20086
SAMPSON ARCHER
Lieutenant Joshua Archer was a son of Sampson and Rebecca (Thompson) Archer. His mother was a sister of General William Thompson. Sampson Archer came from England to Augusta county, Virginia, in 1737. In the year 1758 he was in actual service against the French and Indians, as lieutenant in the militia of that county. He was elected to the vestry of Augusta parish, Staunton, Virginia, November 23, 1756, and in the minutes of a vestry meeting of Augusta parish for May 20, 1761, occurs the following entry: "Sampson Archer, Gentleman, being about to remove out of this colony, has resigned his seat in this vestry". At the time he was one of the wardens. Lieutenant Joshua Archer, son of Sampson and Rebecca (Thompson) Archer, was born in Augusta county, Virginia, during the year 1745.
During his early life he accompanied his uncle, General William Thompson, on his surveying expeditions, and they were the first white men to visit any part of what is now Fleming county, Kentucky, in 1775. They also discovered the Upper Salt Licks of Kentucky. He served in the Revolutionary war under Colonel Arthur St. Clair in 1776, as sergeant in Captain William Butler's company. In 1777 he was lieutenant of a company of riflemen, commanded by Captain John Nelson. He subsequently acted as scout and spy under General George Rogers Clark, and served until the close of the Revolution. He was killed by the Indians near Louisville, Kentucky, in 1800. General George Rogers Clark delivered the funeral oration at his burial. While in service at Carlisle, Pennsylvania, Lieutenant Archer met and married Jane, daughter of Captain Joseph, and Mary (Ferguson) [this maiden name probably an error] Hunter, both natives of Antrim, Ireland, who settled in Cumberland county, Pennsylvania, early in the eighteenth century. Captain Joseph Hunter served in 1779, with General George Rogers Clark, helping to establish Fort Jefferson, near the mouth of the Ohio river. From an article of Thomas Joyes it appears that Captain Joseph Hunter exercised some form of civil and military jurisdiction over the surrounding territory.

Birth

Ca 1754

Father	Joseph Hunter (1730 - 1793)
Mother	Mary Holmes ( - 1784)
Sibling	Mary Hunter ( - )
Sibling	Martha Hunter (1752 - )
Sibling	James Hunter (1756 - 1777)
Sibling	Joseph Hunter Jr. (1760 - 1823)
Sibling	Ann "Nancy" Hunter (1764 - 1807)
Sibling	David Hunter (1766 - )
Sibling	Abraham Hunter (1772 - 1786)