There are several William Widaman's out there which confuses your issue a bit. But here is what I found:

1900 Orlando, Logan County, Oklahoma Territory census:
Widaman, William H., head, 7/1835, PA, PA, PA, farmer, married 31 yrs.
Widaman, Dora, wife, 5/1844, MO, MO, MO, 3 children born,3 children living
Widaman, May, daughter, 1/1880, MO
Widaman, John, son, 11/1888, KS

1900 Olive, Garfield County, Oklahoma Territory census:
Widaman, Ernest, head, 4/1874, MO, farmer

1910 Orlando Twp., Logan County, Oklahoma census:
Widaman, Dora, head, widow, 64, IL
(Both Dora and Ernest's birthplaces change from MO to IL. William evidentally died between 1900 and 1910.)
Widaman, May, daughter, 26, MO
Widaman, John, son, 22, KS

1910 Olive Twp., Garfield County, Oklahoma census:
Widaman, Ernest, head, 36, IL
(The census states that Ernest has been married for 4 years but there are no other people appearing in his household.)

1920 Olive, Garfield County, Oklahoma census:
Widaman, John L., head, 31, KS, farmer
Widaman, Ruby A., wife, 25, IL
(I guess we can surmise Dora died since I couldn't find her listed anywhere on the census data and May, the sister, must have married.)

1920 Oakdale, Noble County, Oklahoma census:
Widaman, Ernest, head, 46, MO
Widaman, Minnie, wife, 49, IN, KY, IN
Widaman, Mame (sic), daughter, 28, OK, PA, KY
(I don't think this is Ernest's daughter as she lists her father's birthplace as PA.)

I couldn't find John and Ruby anywhere on the 1930 census.

1930 Oakdale, Noble County, Oklahoma census:
Widaman, Ernest, head, 54, divorced, IL

The listing for John's WWI Draft Registration lists his name as John Lee Widaman, b. 11/9/1888 in Cowley County, KS, living in Garfield County, OK, farmer, single.

A few other items I found online which I can't verify but seem to fit the pattern are:

John married Ruby A. McInturff who was born 2/24/1897 in Marion, IL, and died 8/8/1978.

John died 5/30/1952.

They had two children.

Hope this helps!

Kim Mohler