Re the origin of the Glover name, as Monica pointed out earlier in the thread, there are a couple of baptisms in Crossmichael, an adjacent parish to Kirkpatrick Durham.
e.g William Clingan 28 October 1766 Parents John Clingan and Grissel Glover.
I note that in the 1841 census there is this entry in Kirkpatrick Durham
William Clingan 70
Mary Clingan 55
Grizzel Clingan 18
Alexander Clingan 15
Agnes Clingan 7
This might be the same William Clingan but hard to prove (note that adult ages are normally rounded down to the nearest multiple of five in 1841).
The 1841 census also has in Kirkpatrick Durham
Janet Clingan b 1876 Scotland
John Laurie B 1830 Kirkcudbrightshire
And in 1851 there is
John Clingan b 1773 mason b Kirkaptrick Durham
Janet Clingan b 1778 wife b Kirkmahoe Dumfriesshire
Janet's details in 1851 do match up with the Janet Clingan showing as Andrew Clingan's mother in the 1861 census. I cannot see a death for John Clingan and so suspect his death was between 1851 and 1855 when stat. reg. began in Scotland.
There seem to be two issues which need to be resolved (if possible!)
1. The apparent discrepancy in the birth date of Grace Glover Clingan between the birth date given for the daughter of John Clingan and Janet Wilson and the date showing on her gravestone.
2. The identity of Samuel Shaw's wife. Nicholas/Mary may be one and the same, Mary being a middle name for example but hard to prove. The book from Wisconsin states that Samuel's widow went there after her husband's death and died there. Might it be worth looking at passenger lists for her?
It may also be worth downloading some records from Scotland's People (it is a pay per view site). My suggestions would be
1. Look at baptisms of the children of James Shaw and Grace Clingan from the Old parish Records.
Sometimes there can be more detail than can be found using familysearch.
2. The death record for Samuel Shaw (should give parent's names, wifes name - the informant's name might also be instructive).
3. The death record for Janet Clingan
4. The will for Andrew Clingan might prove that he was Grace's brother if she is named in it.
5. The death record for Andrew Clingan.
Apologies for such a long post. This is an intriguing puzzle!
William