Ruth,I am a little confused because you show two surnames, both Buckham and Buckman.I can see where either or both could or would be used.That is a little difference compared to most "mis-spellings" I see in my family names.
Anyway, could the following information be your family, and be helpful to you?I don't have enough to go on to make sure it is the same family group, but it looks like they are.
On the 1910 census, in Oakland, Alameda county, California F. Elmer Buckman, head; 27 years old; M1 for 3 years Myrtle, wife; 27, M1 for 3 years, 2 births 2 living children Harold (son) 1-9/12 Dorothy Belle? (daughter) either 8/12 or 3/12
On the 1920 census, in Glendale/Burbank, Los Angeles county, California Myrtle B. Buckman, 36; divorced Harold C. (son) 11 Dorothy B. (daughter) 10
Again, it looks like this is the wife/children of Elmer, but there are a few discrepancies.One, there is also a son, not just a little girl, who was left behind (if this is the same family).Two, of course, would be the surname spelling.
On the 1880, 1900 and 1910 census reports the family surname is showing as Buckman.