You have probably done enough research to know that there are many inconsistencies in what can be found. The profile that you found for Letha M. Rogers seems to have several errors.
Here is what I found in the 1900 U. S. census and it does seem to be your family.
1900 Delaware Co. Iowa
Andrew J. Rogers, b. July 1861 in PA
Carrie L. Rogers b. March 1873, IA
Letha M. b. Sept 1887, IA
Opal V. (mistake in initial) b. July 1890, MO
Roswell R., b. Dec 1894 in IA (this is probably Roland)
Of course, your father had not yet been born.
Carrie L. Rogers father was Eli Wellington Bort, so now you know why your father’s middle name is Wellington. Eli and his wife also moved to San Diego Co. CA.
I found further information. If you would like to see it, please let me know.