Well, yes you do have his birth date, Aug 1886 on the 1900 census.His father, Nathan A. Cooper owns land, and still owns land in 1920.I would check out land and probate records, see who shows up as heirs.If he was living some distance away, Hugh might have given power of attorney for someone to collect his share of the estate, and that would give you where he was living at that time.
If this was my line, I would send for a copy of the application the Hugh on the SSDI filled out for his SS card.The names of his parents, his residence at the time of the applicaton and other data will be on there, too.If he turns out to be your Hugh, then send for a copy of his death certificate, see who was the informant.Maybe he remarried, or even had more children???
One would assume if Hugh was living in Hawaii (last resiedence) he probably died there.He does not show up on CA Dth Idx.
If you do not have Ancestry.com (I do not have it) your local Family History Center has a subscription and you can use their computer to look for Hugh on the 1930 census.Ancestry has an everyname index for 1930 and maybe you can find him.Volunteers will show you how to use the Ancestry.
On the 1930 census Laura and her children are in Navarro Co, TX, looks like she owns her property.Do you know why she moved?She is listed as widow, but I've often seen divorced women list themselves as a widow.Unfortunately being divorced was sometimes frowned upon.