A couple of years have elapsed since this thread was started. It just so happens I was doing a lot of work on the family of Joseph Carter of Paulton recently, in conjunction with another researcher. You may be interested in the conclusions.
There are actually two Joseph Carters of similar age baptised in Paulton, one on 4 Apr 1777 (son of James and Anne) and the other on 27 Mar 1785 (son of Joseph and Prudence). The older Joseph married Margery or Margaret Carter on 25 Dec 1800 (she was buried on 20 May 1812), and the younger one married Mary Bull on 9 Mar 1812. Since the Mary Bull marriage pre-dates the death of Margery, we must be dealing with two different Josephs. Mary Bull is not a second wife of Joseph b 1777.
The following children are all baptised in Paulton between 1813 and 1831, stated to belong to a Joseph and Mary Carter: Grace 31 Oct 1813; Maria 16 Jul 1815; George 12 May 1816; George 24 Dec 1820 aged 3 years 9 months; Joseph 24 Dec 1820 aged 9 months; Isaac 7 Sep 1823; Daniel 22 May 1825; Phoebe 18 Sep 1831. These can’t all belong to the same couple, since both Georges lived to adulthood. Both married in Paulton within ten months of each other, and both were stated to be bachelors, therefore ruling out the possibility of the same person remarrying. One married Elizabeth Chapman on 26 Dec 1842 (witnesses Peter Gregory & Elizabeth Colmer), and the other married Mary Gregory on 7 Oct 1843 (witnesses Simon Gregory and Ann Bull).
It would seem obvious, then, that the older Joseph must have remarried, coincidentally to a Mary. This is borne out by the occurrence of two burials in Paulton - Mary Carter, wife of Joseph, on 4 Apr 1819, aged 34; and Mary Carter, buried 11 Oct 1832, aged 43.
As for the Joseph Carters, one died on 27 Feb 1843 and was buried on 5 Mar 1843. The informant at his death was Peter Gregory. The other Joseph died on 16 Jun 1847 and was buried on 18 Jun 1847. (In a strange quirk, the death certificate gives the surname “Wilkins”, which is mentioned, and corrected to Carter, in the burial register. It's probably just a simple error whereby a name has been mistakenly copied down from the local returns.) The stated ages strongly indicate that Joseph b 1777 died in 1843 and Joseph b 1785 died in 1847.
Peter Gregory married Maria Carter (b 1815, daughter of Joseph) in 1833. Not only is he the informant at the death of Joseph Carter in 1843, he is also a witness at the marriage of George Carter and Elizabeth Gregory in 1842. Logic therefore dictates that Joseph 1777-1843 is the father of Maria, and of whichever George married Elizabeth.
Grace Carter is with the younger Joseph in 1841. This means Grace is not a sibling of Maria, who is a daughter of the older Joseph. Other factors derived from the census indicate that Maria is a sibling of Daniel and Isaac, who were born after 1819, so their mother must be the Mary who died in 1832 not 1819.
The final piece in the jigsaw is a marriage on 4 Nov 1832 in Paulton (which I only discovered the other day): George Gulliford married Ann Carter, spinster, and the witnesses were Peter Gregory, Maria Carter and John Ashman. As usual in this saga, Peter Gregory is the key, a reminder of how incredibly valuable witness details can be. A check through the censuses reveals Ann with her husband George Gulliford in Timsbury in 1841, in Paulton in 1851, in Upper Machen, Monmouthshire in 1861, then a gap, and they are in Marylebone in 1891. Ann is consistently stated to be born in Timsbury, which is where we find this baptism: 8 Aug 1813, Ann, daughter of Joseph and Mary Carter. And also in Timsbury, 14 Oct 1810, Susanna, daughter of Joseph and Margery Carter.
I don’t think there is any doubt that Ann is a sister of Maria Carter who is a witness at her marriage. Her father is Joseph Carter 1777-1843, and Susanna is a child from his first marriage. There is a remarriage too – Joseph Carter, widower, married Mary Carter, spinster, on 25 Dec 1812 at Bath St James.
So by a convoluted route, we know that Mary Bull died in 1819, and Mary Carter nee Carter (who I think is the younger sister of the older Joseph’s first wife Margery, but that’s another story) died in 1832. The younger Joseph, with Mary Bull, produced Grace and George who married Mary Gregory. The older Joseph, via his two marriages, produced all the others.
Sorry for the length of this. It's complicated!