Re: family tree
Jesuph is listed "officially" as Rzeszow on my father's (born 1900) immigration certificate (originally occurred around 1923) from an 80's recreation by the Ellis Island restoration committee which I have framed here on my wall.(I'm 61.) What I'm saying is that Rzeszow is my father's family's hometown also.(The Jewish name is Reishe - my spelling.)My father was also Baruch, probably named for the same prior relative as your father.My father's father was Mendel (born about 1880, with official name Nachman Menachem).Mendel was the youngest of 6 children, and he came to New York in 1911, and was considered a bit of a rebel for being the only Teitelbaum to come to America at that time.One of Mendel's 2 older brothers (he had 3 even older sisters) was Rabbi Menashe, who had 2 known sons, Shmuel and Mordechai.Shmuel had 2 sons Moshe (older) and Ahlter.This Ahlter, I believe came to New York around 1960 from Europe, because I met him many times when he came to visit us.I don't know yet how old you are, but I believe this Moshe is your great-grandfather.
See if this fits in with your father's recollections.
your cousin (very likely, even if not exactly this way)
Yerucham (we made aliyah from upstate New York to Israel in 1999)