In short, I had my Dad's y-dna tested and the most likely surname that I could glean from those results was McLaughlin, probably from Ireland. Recently I have finally found three people, who are dna matches to my Dad, who also all descend from one Daniel McLaughlin from a small town called Magilligan in Derry, Northern Ireland.
Ancestry tells you how many centimorgans (cM) of dna you share with each of your matches. With this information and some handy dandy charts that I found online, I was able to calculate the amount of dna these matches WOULD share with Dad if Daniel McLaughlin was Dad's great-grandfather. It was well within range of the amount shared with these matches! So, I have concluded that the "mystery man" almost has to be Daniel McLaughlin. If it were a brother or cousin, the amount of dna shared would be much lower. And it couldn't be his father or his son, since the time frame would not match up with when John Reid was born.
I do know that Daniel McLaughlin was married and had six children with his wife, Elizabeth Cummins. His second child was apparently born in Scotland, not far from where Caroline lived, in 1868. Most likely he had found work in Scotland, as many Irish did, and took his wife and their first child with him. But, the family returned to Ireland, because the rest of his four children were born there. Only three of his children reached adulthood, and all three emigrated to the United States.
That is all I know about Daniel. I do not know who his parents were, any siblings he may have had, or what he did for a living that may have brought him back to Scotland in 1871, leaving his family behind in Ireland. On two of his children's birth records, it says "labourer" for occupation, but that could mean almost anything.
My theory is that his parents were named John and Mary and that he was born in 1844. That John's parents were Patrick McLaughlin and Mary Spence, who appears on at least two of the match's trees. But that remains to be seen. I paid for the death record one week ago and am waiting impatiently for it. Will update!