There's a definite mention of Sarah Britton's wedding in an 1820 letter from Rachel Mordecai to her brother Solomon:
"If you feel inclined to laugh, look into the Enquirer of the 22d & you will find the marriage of Ellen Lady of the Lake, alias Sarah, daughter of William Britton esq, to, not Malcolm Graeme, but James fitzJames, alias Dr. Bouldin. Never did I imagine that Scott's beautiful lines could be so sadly misapplied, or could be made to appear so superlatively ridiculous."(letter dated 24 February 1820, Jacob Mordecai Papers, Duke University)
From this passage, a reader will get a good sense of the tart way the Mordecais sometimes talked about their former students (not just poor Miss Britton). This was not, apparently, a beloved or admired young woman in their conversations. But it certainly gives solid leads about her adult life! In another letter, there's mention of a "Miss Britton" going to the Virginia Springs for her health in July 1817 (Ellen to Solomon, 24 July 1817, Mordecai Family Papers, Southern Historical Association).
From there, we have no trouble locating these sisters: Sarah and Mildred Britton both married Bouldin men, brothers: Sarah Barksdale Britton married Rev. Robert Ephraim Bouldin (1795-1881), and Mildred W. Britton married Stith (Seth?) Bouldin (1797-1867); and apparently the both married in 1820: Sarah in January and Mildred in July. (Mildred may not have lived long after she married; her husband had a second wife, one of Mildred's cousins, Lucy Pleasants.) A family bible belonging to Sarah's descendants gives her birth as 1802, and her death as 1884; and shows her having three daughters, Elizabeth (1825-?), Margaret (1833-1878), and Henrietta (Etta; 1835-1908).
So now, we see 14-year-old Sarah Barksdale Britton and her younger(?) sister Mildred, daughters of William Britton and the former Elizabeth "Betty" Thweatt of Virginia, arrived at the Mordecai school in January 1817. One of the girls left for health reasons in July, but returned to finish their three sessions there in mid-1818. Two years after they left school, 18-year-old Sarah and her sister Mildred had married brothers; Sarah had three daughters, while Mildred may have died young.
Why did the Mordecais have such a mocking tone about Sarah Britton in 1820? No idea; that's the kind of information that generally can't be teased out of genealogical data.