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I looked wherever I could think of, and I didn't see any likely matches.  There are links to various NY City death records here - https://www.deathindexes.com/newyork/city.html 

It's possible she could have died elsewhere, so I would say if there are any other relatives in other states, check for her there.  There are gaps in the New Jersey death index in the 1940s, and some of the New York state death index from the 1940s is hard to read, so those are possible explanations for her not showing up.

If you can find where her children are buried, see if she is buried with them. 

It looks like this may be Charles' death record, which was signed by Rebecca on the 2nd page.  https://a860-historicalvitalrecords.nyc.gov/view/5522925

He was reported to be buried in Mt. Zion Cemetery per the death certificate and an entry on Find a Grave.  I didn't see Rebecca buried with him per the cemetery's website.  http://www.mountzioncemetery.com/

Son Isidor's WWII draft registration card from 16 Feb. 1942 has Dr. Abraham Handelsman listed as the person who would always know his address and Isidor's address changed from 2940 Ocean Ave. Brooklyn to 1412 Ocean Ave. as of 27 Jul. 1942.  Maybe that means Rebecca had died by then?

It looks like the cousin mentioned on the passenger list is Annie Godwin.  Her address for the 1900 census looks like 538 Beech St., Scranton, PA. https://www.familysearch.org/ark:/61903/3:1:S3HT-DH2D-3G?view=index&personArk=%2Fark%3A%2F61903%2F1%3A1%3AM33Z-GBG&action=view&cc=1325221&lang=en

A possible obituary for her lists some McLaughlins in the family.  https://www.newspapers.com/article/the-times-tribune-obituary-for-patrick-g/164990629/

In that era, the Catholic Church (among other religions) was publicly resistant to civil registration of marriages in NY City, so sometimes the priests deliberately did not register the marriage.  Also, sometimes the papers didn't get filed with the city by mistake.

My husband has ancestors who were also from Ireland and married in NY City in 1901.  I got the church record from Find My Past (they used to have the images of parish marriages, but they were later removed & now it is just a transcription), but I have never found a civil record despite looking in the places mentioned above by oldohiohome in every possible combination I could think of. 

You can order the church record from the Archdiocese of New York for a fee - https://archny.org/ministries-and-offices/archives/genealogy/

Brooklyn Eagle is available for free through the Brooklyn public library's site - https://bklyn.newspapers.com/

If that doesn't work, try www.fultonhistory.com, which has many free papers from Brooklyn & elsewhere.