Hi Amy Booth. You are rght, this family is a wee bit off here. My 4th ggrandmother was Catherine Hay Selby 1780-1830, daughter of Adam, 1738-1803, Hay/Hoh. They used both variations on the last name. Adam, along with his brothers, Michael (John) 1733-1810, Valentine 1735-1832, Simon 1742-1842, Francis/Frantz 1745-1826 and William 1755-1793 came to America from German from where the families had been living since John Hay 1635-1704 left Scotland because of the unrest over religious differences. That is the reason for the 100 year gap. I am not sure if any of the other members of the family moved at the same time or not. I wasn't able to find any relatives related to Richard in my family so I am not sure if there are others from there that could have another family.
The "K" middle initial is interesting. I saw several with the same initial and it was always a bold "K". So I am stumped on the one too.
As for the Rurk family taked Richard in, it could be they took him in as a farm hand, especially since they were both in their 50's and probably had a hard time working without help or little help. That is a common practice back then. My grandfather was made to go live with a family to help out on a farm. He had to quit school so he never got to finish school, which was a shame because my grandfather was very smart.
Richard did marry Hanna Ann Suit. You may have this but I will give it to you in case you don't In the 1870 United States Federal Census, they list Richard and Hannah as living in Chenoa, McLean, Ill. Hannah was born in 1842 and died in 1882. they had four children as of 1970 census. Ida B.Hay, age 9, George W., age 6, William Hay, age 3, and Alonzo Hay, age 1. They could have also has others. I just don't know.
OnFind a Grave I found a tombstone at the Ebenezer Cemetery in Hamilton Co., Ohio. It is plain with Richard Hay, 1839-1897 and Hannah A. Hay, 1843-1822 engraved on it.
I am hoping some of the information may help you to move on. I know it is frustrating to not find information, but there just isn't much to go on. Wish I could have been a little more helpful. Good Luck. Marilyn Humrichouser Albert.