Larry This is a fantastic posting which shines a clear light on the relationships, and of course raises questions and possibilities. I'm not sure I have absorbed it all, but I will start with a query.
You say "If Love had moved in with Thomas V and Sarah, it would help prove Sarah to be her daughter. Thomas V wouldn’t have been Love’s son, for Thomas who married Mary Stokes is documented in Madison Co with Love and John Province in 1814."
The first sentence I get and agree with. For the second do you mean "Thomas V.....son, for it is the other Thomas Province, the one who married Mary Stokes, who has Love and John Province with them in 1814."? This is a small point of clarufucation, though the principle of a parent living with a child and not a more distant relative is important.
There are two big points for me. Who are the parents of Thomas [without the V] Province? You are switching from William P and Rachel Cooper to John P and Love Swain Barnard. I think your argument is very strong. Another straw in the wind (which by itself is not that important) is that Thursy Barnard, a grandaughter of Thomas [without the V] and Mary Stokes, does not apparently know about her great grandparents. The first set of possibilities, William and Rachel are dead by 1847 & after 1867 respectively. The second set are John and Love who are dead before 1840 and after 1840 respectively. The death certificate of my great great grandmother Suzannah Barnett daughter of Susannah Love Province has Suzannah Barnett born in Texas. This is wrong, but why did my great grandfather think that his mother was born in Texas? Well, Love Swain Barnard died in Texas after 1840. So I am saying that it would have been harder to remember John and Love compared with William and Rachel, and that there is a Love Swain Barnard link to Texas. This is pretty weak stuff, but it fits your conjecture.
The second point is that your argument explains the existence of the family Christian name Brazilla (variously spelt and Love. My Brazilla Barnett [or Barnard] marrying a Susannah Love Province/Provence and the close existence of a Love Barnard and an older Brazilla Barnard (b 1764) cannot be co-incidences.
My ggg grandfather Brazilla Barnett/Barnard could be a grandson of a number of Timothy Barnard and Love Swain's children. I believe "Brazillai" Barnard had at least three children: (1) Timothy. Born in 1798 in TN. In 1820 when Timothy was 22, he married Elizabeth Daniel, in Madison, AL (2) Jane. Born ca 1810 in TN. In 1856 when Jane was 46, she married Joshua Young, in Madison, AL. (3) Martha born in 1812 in TN. Martha died in Colorado, TX, on 30 Dec 1851; she was 39. In 1831 when Martha was 19, she married Albert Calhoun Taylor, in Huntsville, AL. See http://homepages.rootsweb.ancestry.com/~sam/gbarnard.html#P33681http://homepages.rootsweb.ancestry.com/~sam/gbarnard.html#P33681 for this information.
I'll have more to say, but Larry I think you have well "staked out" the issues relating to this family tree.