You wrote: iv. JOHN HAMILTON was born after 1850. He died date Unknown. He married Mary Shaw date Unknown. She was born date Unknown. She died date Unknown.
John W. Hamilton and Elizabeth Musselman had the following child:
v.EDWARD HAMILTON was born about 1872 in Ohio. He died date Unknown.

I have a John W. Hamilton (1.5.1846 - 8.21.1909) in my family tree. He married Mary E. Shaw (7.22.1855 - 5.1.1928) in 1875. I do have some contradictory information about this couple that I need to look into.
I do show he had another wife named Elizabeth but no children named Edward.