In 1910 Dayton and Jessie were living in Baltimore, Henry Co., IA.
Dayton H Parsons, b. IA, 22, marr 11/12ths, retail merchant general store.
Jessie L. Parsons, b. IA, 22.
Walter T. Parsons, boarder, b. IA, 24, single, retail merchant general store.
I couldn't find them in the 1920 Censuses.
In 1930 Jessie and her boys were living in Seattle, King Co., WA.
Jessie, b. IA, 40, widow, clerk pharmacy.
Herride/Herrick, b. WA, 15.
James, b. WA, 13.
Raymond, b. WA, 11.
A Herrick C. Parsons b. 9 Nov 1914, Last Residence-Seattle, King Co., WA 98126 died 22 June 1990, Last Benefit Mailed to=Seattle, King Co., WA 98136. His soc. sec. # was assigned in WA before 1951. Source: Social Security Death Index, www.ancestry.com.
The King County records will be loaded into the Washington State Digital Archives soon. I'm checking on the date for you. Then more information on your family should be available.
You might want to contact the Seattle Genealogical Society, www.rootsweb.ancestry.com/~waseags/ who does research. They can check for the boys and Jessie in the Seattle Directories.
Also you can request copies of Jessie and Herrick's obits from Random Acts Genealogical Kindness. Go to www.raogk.org, read instructions, choose Washington, choose King Co.
Also they are available from the Washington State Library, www.secstate.wa.gov/library/ask.aspx . They will search the newspaper microfilm for 60 minutes at no charge and email what they do or don't find to you. Takes about two weeks. Successful Searching!