Ok, I think I've found some of the family in the 1920 Census; did Rose marry a Henry SHAPIRO?
1920 Pennsylvania, Philadelphia Ward 39 District 1411 House No: 544 (so probably the same address as they were residing when naturalisation was applied for)
Abraham LUPINSKY (mis-transcribed as Tupinsky

)
Head
Age: 51
Year of immigration: 1905
Naturalised Alien : 1913 (same date is on the back of the naturalisation papers when it was finally processed in court)
Born: Russia; Mother Tongue: Jewish
Father born: Russia; Mother tongue: Jewish
Mother born: Russia; Mother tongue: Jewish
Can read, write & speak English
Occupation: Operator, Ladies W?
Rebecca LUPINSKY
Wife
Age: 54
Year of Immigration: 1906
Naturalised Alien: 1913
Born: Russia
Mother Tongue: Jewish
Father Born: Russia; Mother tongue: Jewish
Mother Born: Russia: Mother tongue: Jewish
Cannot read or write English
Rose SHAPIRO
Daughter
Age: 22
Year of Immigration: 1906
Naturalised Alien: 1913
Born: Russia; Mother Tongue: Jewish
Father born: Russia; mother tongue: Jewish
Mother born: Russia; mother tongue: Jewish
Can speak English
Henry SHAPIRO
Son in Law
Age: 26
Born: Penns(ylvania); mother tongue: English
Father born: Russia; mother tongue: Jewish
Mother born: Russia; mother tongue: Jewish
Can read, write and speak English
Occupation: Accountant, ? Store
There is an Abram RAPINSKI on board the Darmstadt, aged 38 (so born c1866), occupation tailor; can read and write; nationality Russian; race Hebrew; looks like he came from Boisan; going to Philadelphia; he had $65 dollars; been to the US before in 1890 or 1892; who he was going to stay with has been crossed out - it looks like xxx Rapinsky in Philadelphia - and friend Hersch Korenfeld has been written in. He appears to be accompanied by a son, Faima? aged 17.
That's the closest I can find in the lists. The dates Abraham gave in his naturalisation application for the Darmstadt leaving Bremen and arriving at Baltimore are correct.
Kind regards
Gaie