It appears that George may have only had the one child.The New Orleans Death Index has an entry for him:
George Vennemann, age 33, white, d 05 Aug 1899 in New Orleans. Volume: 120Page: 178
From the New Orleans Marriage Index: Lillian Catherine Vennemann, age 19, married Anthony Sebastian Roberts, age 26 on 14 Apr 1918 in New Orleans.Volume: 40 Page: 977
Here are Lillian and Anthony in 1930 1930 Louisiana, Orleans Parish, New Orleans, ED 156, Page 7A. Dwelling 114/Family 115.4021 Iroquois (rent $10) Anthony S Roberts, head, white, 37, married, age26 at first marriage, reads, writes, he and father b LA, mother b Alabama, carpenter, out of work 34 weeks in 1929. Lillian, wife, white, 31, married, age 19 at first marriage, reads, writes, she and parents b LA, inspector at overall factory Warren, son, 9, attends school, b LA Marvin, son, 5, attends school, b LA
The SSDI has Warren N Roberts, b 27 Oct 1920, died 25 May 1997 in New Orleans.SSN 439-05-0447
You might want to order Warren's death certificate.It will give the name of his wife, which can help you track down his children.You might also check to see if he had an obituary.