You didn't mention the names given on each gravestone for the father. It may also be possible that one gravestone has a Yiddish name for the father (kinnui), another has a Hebrew name (which would have been their formal religious name). For example, someone known as Leib (always a possibility for someone who takes the name Louis) could have a Hebrew name of Aryeh (both meaning "lion"). Another example, using my great-grandfather and his brother: one's gravestone lists his father as "Shimon Leib," the other gives his father's name as "Shimon Yehuda." With Leib being Yiddish for Lion, which was the symbol of the tribe of Yehuda, it is possible to understand how both names might have been viewed as fitting the same father. Or Louis Gottstein may have originally had a double name (for example, Aharon Leib), and ended up with "Leib" on one gravestone and "Aharon" on the other. These alternatives should be explored as well as the possibility that Nathan and Solomon did not share a father.
All the best,
Jay Paul, PhD
San Francisco CA 94117
Researching: SUMBERG (Pilvishok/Pilviskiai, Lithuania), LANGERT (Pilviskiai & elsewhere in Suwalki gubernia); KAHN (Ranstadt, Germany), GOTTLIEB (Grebenau, Germany), PAVLOVSKIY / PAVLOVSKY (Mala Antonivka, Bila Tserkiv, Vasyl’kiv, Kyiv gubernia, Ukraine), LEVITSKIY / LEVITZSKY (Yasnohorodka, Vasyl’kiv, Kyiv gubernia), KOTLER (Vistytis, Suwalki gubernia), WOLF (Austro-Hungary).