William Herbert Puryear married Phoebe White 10/26/1880 in Pottawattamie County, Iowa. She was born 4/11/1862 in Illinois. She and William are in the 1880, 1895 (state), 1900, 1910, and 1920 census for Pottawattamie County.
I do not know who Alvira was married to before William. The 1930 census for Monroe County says that she was first married at age 25. She is living with her parents in the 1885 state census.