I used to live in Charlestown and worked at the Charlestown Public Library. If you haven't you need to go there as they have a great deal of information about Jonathan Jennings. At least two dissertations have been written about Jennings and when I lived there in the 1980s a resident, now deceased, did a lot of research and led the movement to put his grave in a better spot in the local cemetery.
Jennings did not have children of his own. Who Clarissa was and where she came from and where she went was a mystery to us back then. She reportedly came from or went to Paducah, KY after his death.
A strange newspaper article came to light while I worked there that was published in the Cincinnati newspaper in the 1820s or 1830s. I cannot remember exact details, but he sounded like a dissipated man... He had a farm a few miles from town and produced whiskey. Whiskey was a good cash crop, but apparently he liked to drink it too much as well as alcoholism is what killed him.
All this and more can be found at the Charlestown Library. I used to know the head librarian well but she has retired. I am sure someone could be of assistance if you cannot get there yourself.
Interest may intensify in Jennings in the coming years as Indiana will celebrate it's bicentennial in 1816.
I tried in vain to track down the miniature he gave Ann, but it seems to have been lost after 1966 when it hung in the Governor's mansion!
Wish I could help more.