Hi:
There is no David Bradford born in Van Nuys (LA County in 1926), however there is a David Bradford born 22 May 1926 in Inyo County as "David Junior Bradford" with mother's maiden name of Kerr.
There were only 2 male Bradfords born in 1926 in LA County where Van Nuys is located: James Slater Bradford, 23 Apr 1926, mother's maiden Hartley, and Joseph Jerome Bradford 22 Mar 1926, mother's maiden Ryden.
Following the family story that there were multiple siblings I checked Ryden and she only had what appears to have been one other child in 1920....Jack R. Bradford, 7 Aug 1920 (can't be sure if this is the same Ryden mother). In checking out Hartley I find: Wayne H, 4 Nov 1923, Jean E., 1 Dec 1924, James Slater, 23 Apr 1926, Ethel Lucile 8 Oct 1927.
I looked at LA newspapers during the period for Bradford and "accident" and "automobile" and didn't get any hits.
Do you have an exact birth date for your father?