You may already have the US Census data for this family; but, I'm posting it anyway for the benefit of other family members and the bonifide volunteers that might wish to help.
After my searches, I also am posting family tree's posted on Ancestry by others. A couple of these trees have a LOT of information (#'s 3 and 4, below). I'd suggest contacting them about this family. It appears there will be many living cousins.
The 1860 Census for Tooele, Tooele County, Utah Territory. enumerated 29 August.
White, William, 52 (circa 1807/1808), born in Pennsylvania, a farmer
Mary 39, (circa 1819/1820), born in Ohio
Sarah 10, (circa 1849/1850), born in Ohio
Alma M 8, (circa 1851/1852), born in Ohio
Phebe 4 (circa 1855/1856), born in Utah
Joseph 1, (circa 1858/1859) born in Utah.
The 1870 Census for Moroni, Sanpete Co, Utah Territory, enumerated 7 June.
Mary White, age 50, born in Ohio
Pheobe (could be written "Pheabe"), age 14
---the family above
Alma White, age 19, born in Ohio, Farmer
Rose, 18 (could be 28?), born in England
Rose, 4, born in Utah
Sarah A 5/12, Utah. Born in December 1869 (per census)
The 1880 Census for Moroni, Sanpete County, Utah, enumerated 7 June.
Mary White, age 69, born in Ohio to both parents born in New Jersey
Joseph White, 21, Utah, Laborer
---next family down
Alma, 27, born in England
Rose 30, born in Utah to father born in New York (not a daughter of Alma), mother in England
Sarah Alice 11, born in Utah to father born in Ohio
Ka(page torn) 6
The 1910 Census for Battle Ground, Custer County, Idaho, enumerated 19th/20th of May
Joseph, age 51, born in Utah to father born in Pennsylvania, mother in Ohio, farmer, married 30 years
Mary A, age 48, born in Utah to both parents born in England
J. Orlando, son, age 27
Okay Burdett, son, 12
Wm Lile(?, unsure due to handwriting), son, age 9
?Samele? Earl? 5
---Based on the 1920 Census, it appears the census enumerator couldn't spell the names?
The 1920 Census for Battleground, Custer County, ID, enumerated 16 March.
Joseph White, age 60, born in Utah to father born in PA, mother in Ohio
Mary, age 58, born in England
Orlando, 34, (it "appears" there might be a "7" written over the "4" for age)
Oakie B, 22
The 1930 Census for Mackay, Custer County, ID
Samuel E White, age 24, born in Utah, laborer/Quartz Mine, first married age 23, renting for $10.00 a month on Pine Street.
Hazel H, age 19, first married age 19
--next family down
Orlando White, age 44, born Utah to both parents born in Utah, laborer/Quartz Mine, first married age 42
Mamie, age 36, born in the Irish Free State, immigrated 1911.
Francis M. Perne, Step-son, 12, born in Montana to father born in Germany, mother in Irish Free State
Joseph J, step-son, 11, born same as above
Marie A, step-daughter, 9, born same as above
Raymond E, step-son, 6, born Idaho, father/Germany, mother/Irish Free State.
I did a quick search on www.findagrave.com
and found the grave stones of Joseph and Mary:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=wh...
Samuel's cemetery, but not grave stone:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=wh...
Family Trees found with the Joseph White Family:
identifies he was born 9 April 1859 in Camp, Utah, died 25 Nov 1927 in Mackay, Custer County, ID. No other information.
same as above
This tree shows a lot of detail, suggest you contact this person.
--It shows Joseph's wife, Mary Ann Ames, died 24 Feb 1926 in Chilly, Custer County, ID.
--His data shows children and grandchildren info.
Also a lot of information.
has information, but some of the children's names are duplicated and wrong.
Tree is by the same person as #5, with little info.