Okay, here is the family of John & Phebe Hagerman, as far as I can tell from Census records, deeds, etc., this also assumes that John wasn't married before and Phebe is the mother of all the children.
1.Catherine, born about 1812, d. before 1850, m. John Talmadge in Monmouth County 8/20/1829.They moved to Bergen County.By 1850, John Talmadge was married to Abigail so I'm not sure if John & Catherine had children, since the children listed could be from either Catherine or Abigail.
2.Hester,(Esther),born about 1811, d. 2/27/1856, m. David Morton, 3/17/1830,in Monmouth County, they are buried at Hamilton Cemetery.Their children included:
John Hagerman Morton, b. about 1830
Mary J. Morton, b. about 1834
Lockwood H.b. about 1836
Thaddeus B.b. about 1838
Elam L.b. about 1842
Nicholas P.b. about 1844
Sarahb. about 1849
3. James Hagerman, born about 1813, d. 8/10/1863, buried Hamilton Cemetery, married Catherine Herbert, 7/12/1834, Monmouth County.Their children:
John Henryb. 1835, m. Sarah Allgor
Emmab. 1839, m. Saxon Raymond
Danielb. 1841, m. Hannah Morris
Catherine A.b. 1843, m. Timbrook White
Sarah F.b. 1846
James M.b. 1849, m. Annie
Marrietteb. 1855, m. Benjamin Harris (I think).
George E.b. 1859, m. Elizabeth White
(Of these children, Daniel, Catherine & Sarah all died at a relatively young age and are buried at Hamilton Cemetery, also Emma and her husband Saxon Raymond are buried there).
4. George L. Hagerman, m. Eliza White, I already gave you the list of his children I found in Census records.
5.John P.L. Hagerman, b. about 1825.Moved to Wisconsin in 1850s.I have a note that he married Mary Harmon in Kenosha Wisconsin, 3/12/1856.He later appears on the 1860 Census in LaPorte County, Indiana with wife Mary and children;
William E, born 1857
Annie, born 1859 or 1860.I haven't traced them any further.
6.Jane, born 1829, d. 3/28/1882, married Eden Howland in about 1849, in Monmouth County.Their children;
Florinne, born 1852
As you can see, no Barnce in the grandchildren of John & Phebe Hagerman.Thus I don't think Barnce and Eleanor Hagerman were from this family...Of course they could be cousins, at some level, since I don't have information on John & Phebe Hagerman's parents.
I hope this helps sorting them all out.