According to one list there were 11 children born to this marriage - multiple sources identify 7 children

Dirck Barent Van Hoorn
1680-1768
Jacobus Barentsen Van Horn
1680-1775
Christian Barentsen Van Horn
1681-1751
Pieter Barentson Van Horn
1686-1749
Nicholas Barentsen Van Horn
1688-
Barent Barentsen Van Horn
1691-1779
Johannes Hoôrn Van Horne
1692-1758
Abraham Barentsen Van Horn
1695-1773
Jannetje Van Horn
1697-1719
Isaak Barentsen Van Horn
1698-1760
Benjamin Barentsen Van Horn
1705-1714

History of Bucks County, Pa Volume 3 by William H. Davis
http://pagenweb.org/~bucks/BIOS_DAVIS/vanhornfamily.html
Peter joined his half-brother, Barant Christian VAN HORN, in his purchase of land in Bucks county in 1703.

2. Barent Christian VAN HORN, eldest son of Christian BARENTS and Jannetje JANS, as before stated was probably born in Holland, a theory which is borne out by the early date at which he acquired title to land. On March 26, 1667, Governor Philip CARTERET granted to Barent Christian, of Menkaque, planter, fifty acres of land at Pembrepach and eighty-five acres on the bay called Kill Van Kull, both in Bergen county. On September 29, 1697, he obtained a grant from the proprietors of East Jersey, 160 acres on "Hackingsack River," joining that of his half brother, Thomas Lawrenson . On May 15, 1703, Barnard Christian, and his half-brother Peter Lawrence, purchased 1,000 acres of Robert HEATON, on Neshaminy creek, in Bucks county, which on September 18, 1707, they partitioned between them. Two days later, September 20, 1707, Barnard Christian conveyed his portion to his two sons, Peter and Christian Barnson, Peter receiving 257 acres and Christian 294 acres. On September 29, 1707, Barnard Christian purchased 550 acres in Bucks county, of Thomas GROOM, 274 acres of which he conveyed to his son Barnard Barnson, June 17, 1714. He also acquired other land in Bucks county, and on June 2, 1722, conveyed to his son, Isaac VAN HORN, 276 acres, and on May 6, 1722, 290 acres to his son, Abraham VAN HORN. He thus owned in all 1381 acres of land in Bucks county, though he continued to live in Bergen county, New Jersey, and died there in 1726. He married, in 1679, at the Bergen Dutch Reformed church, Geertje DIRCKS, daughter of Dirck CLASSEN, who was baptized in New York, March 5, 1662. The children of Barent Christian VAN HORN and Geertje DIRCKSE were:

1696 - Bergen Co NJ, Quit Rent Twp, Charistianse Van Horn

More info is in "A Lutheran Mission in Northampton Township in 1748" from an
article in 1926. I think this was presented in an early proceedings of the
Bucks County Historical Society. pgs 45-47.

From History of Bucks County, pg 93:
Barent Christian Van Horn, eldest son of Christian Barents and Jannetje Jans,
as before stated was probably born in Holland, a theory which is born out by
the early date at which he acquired title to land. On March 26, 1667, Governor
Philip Carteret granted to Barent Christian, of Menkauque, planter, fifty acres of land
at Pembrepach and eighty-five acres on the bay called Kill Van Kull, both in Bergen
county. On September 29, 1697, he obtained a grant from the propreitors of East
Jersey, 160 acres on "Hackingsack River," joining that of his half brother Thomas
Lawrenson .

On May 15, 1703, Barnard Christian and his half-brother, Peter Lawrence, purchased
1,000 acres of Robert Heaton, on Neshaminy creek, in Bucks county, which
on September 18, 1707, the partitioned between them.

Two days later, September 20, 1707, Barnard Christian conveyed his portion to his
two sons, Peter and Christian Barnson, Peter receiving 257 acres and Christian 294
acres.

On September 29, 1707, Barnard Christian purchased 550 acres in Bucks county, of
Thomas Groom, 274 acres of which he conveyed to his son Barnard Barnson, June
17, 1714. He also acquired other land in Bucks county, and on June 2, 1722, conveyed
to his son, Isaac Van Horn, 276 acres, and on May 6, 1722, 290 acres to his
son Abraham Van Horn.

He thus owned in all 1381 acres of land in Bucks county, though he continued to
live in Bergen county, New Jersey, and died there in 1726. He married,
in 1679, at the Bergen Dutch Reformed church, Geertje Dircks, daughter
of Dirck Classen, who was baptized in New York, March 5, 1662. The children
of Barent Christian Van Horn and Geertje Dirckse were: etc...

http://genforum.genealogy.com/vanhorn/
http://jerrie.vanhorn.com/

the complete text from the Bucks County PA History is at:
http://www.rootsweb.com/~pabucks/vanhornfamily.html

https://books.google.com/books?id=-nEHRwRAwxAC&...20Dungan&f=false