If the McColgans went to KY in 1780 it was probably to Lincoln County where someone in the family had a land grant.I say Lincoln because Green County was not formed until 1793 - and it was formed from Lincoln and Nelson Counties [both of which are original counties - however, most of the land grants were in Lincoln.It would appear that Thomas McColgin died in Green County and son John was raised by his grandfather, John.Hamilton may have been bound out to learn a trade.There should be guardian records or records of being bound out as well as periodic reports to the court.
I believe that John McColgin, the son of Thomas & Sarah was in Hamilton County by Sep 24th 1837 when -John and Mary Caterine McColgan sold land to Hugh White who married his sister in 1829 in Hamilton County.
The Goshen Trails Magazine, in Hamilton County, some 30 or 40 years ago published an account of the families coming to Hamilton around 1825.Included were several Moore's including Jesse whom it said came to Illinois with several grown sons.[I believe they included William, Jesse Allen, Isaac, and Emory Wilson].
I would think that Sarah married Thomas around 1813 or '14.With her born in 1798 and her oldest daughter getting married in 1829, we can make them both around 15 when married.The marriage should be in Green County. I also believe that Sarah should have married William Vaughn about 1824 in Green County, too.
Green County would then become the most likely place for Jesse Allen Moore, Sr, born 1802, married c1824 to Elizabeth Vaughn and both families came to IL by 1825 where the widow and widower married each other in 1836.
Now, when are you leaving for Green County??We won't be going until June.That might be the County with Coffee Trees all around the Court House. At least one History of Green County has been published.