I don't know if I ever answered this message or not. However, I cannot find any information on Joseph William Calhoun 1807-1880.
Our Calhoun Family Vol.1,Pg.731&732 However, you mentioned a John Calhoun & Rebecca Rand. I found a Thomas Calhoun 1735-1772 & Rachel Peck b.1754. They had a son John Calhoun b.1770 and he married Rebecca Rand in 1790. They had 12 children all born in New Brunswick. There is no son named Joseph b.1807.
I don't see any connection between them and Joseph William Calhoun 1807-1880.