Joseph Hill married Catherine Hill in Starksboro, Vt on 1 Apr 1817. Catherine is his cousin. However, they both died and were buried in Starksboro, Vt. They had nine children not three. They did not move to Illinois. I'm not sure this is the Joseph Hill you are looking for.
The Starksboro Historical Society has a website. And in the next town over, in Bristol, Vt is a local historian, John Burbank and his email is firstname.lastname@example.org
He has information on a lot of families. John maybe of help in your quest.
If you do think this Joseph may who you are looking for, I'll continue sending you what information I have.