The only Byron Hoag (b: about 1857) I have was the s/o Othniel Hoege and Althea Ura Pelton (Othniel's parents wereElizabeth LeMunyan and John Hogg) who first married Eliza Jones in 1870 then Elizabeth Horton in 1877.Elizabeth was born in Lenawee Co. on 2 Jan 1860.I didn't find a daughter named Addie, but in the 1870 census I found their son Alven and daughter Orlina.In the 1880 census Alven was not with them, but another son, Silas was aged 7.They were living next to Geo. Hoag and his wife Jane in Scipio, Hillsdale, MI.
Byron's siblings were: Cyrus Hoag, b: 1849, m: Martha White
Alva Hoag, b: 1853, m: Ella Metcalf, in 1880 they lived in Geneva Twp., Van Buren Co., MI
Minnie E. Hoag, b: 1864 in Van Buren Co., MII'm sure all these birthdates are estimates.
I haven't verified any of this information (except the census records), but it may give you another lead along the way.
In 1860 Byron was living with his first wife and a 4-year-old child in Morenci, Lenawee, MI
In 1870 Byron and Eliza were living with their children Alven and Orlina in Reading Twp., Hillsdale, MI
In 1880 Byron and Eliza were living with their children Orlina and Silas in Scipio, Hillsdale, MI
In 1900 Byron and Eliza and their daughter-in-law Harriet were living in Scipio Twp., Hillsdale, MI
In 1910 Byron (76) and Eliza (72) were living alone, still in Scipio Twp., Hillsdale, MI.Living right next door was Silas and Harriet Scipio, Hillsdale, MI with their daughter Violet M. (13y) and son Gerald (10).