When Bluma came to US with her two sons I see they arrive NY. Do you know if they immediately went to New Jersey? I ask because at ancestry.com there is a death for a David Bernstein Dec. 23, 1892, age 3. I wondered if this could be your fellow.
New York City, Deaths, 1892-1902 about David Bernstein Name: David Bernstein Birth Date: abt 1890 Age: 3 Death Date: 23 Dec 1893 Death Place: New York, New York Certificate Number: 43654