Hi. Just came across this discussion. As is usually the case, the whole Daughety-Daugherty-Daughtrey name thing is more complicated than we would like it to be.
I've been working on a book for several years tracing the descendants of Owen Dogharty (about 1656 - 1712).
The name in Ireland when he migrated to Norfolk, VA, was "Dogharty." Various documents in VA spelled his name perhaps 20 different ways--Dockerly, Dougherty, Doiety, etc. His son Owen II spelled his name "Dougharty" most of the time--or the recorders of his documents did. By the time Owen III moved from Norfolk, VA, to Craven County, NC, his name was spelled pretty consistently as "Daughety."
Yet the descendants of their brothers/cousins who resided in Johnston Co., NC, spelled their name "Daughtrey" most of the time--or the recorders of the documents did.
Owen III had two families. The 5 children of the first family remained in NC and continued to spell their name "Daughety." They still do today. The 5 children of the second family mostly migrated to KY in 1797. At first, they spelled their name "Daughety," but within a generation or two, had changed the spelling to "Daugherty."
Only one member of that second family remained in Craven County, NC, and, fairly quickly, his name was normally spelled "Daugherty." His descendants still spell the name that way today.
What I'm trying to say to you is that these were all members of the same family--all Irish. But their names were spelled differently.
Does that mean that what you said about the English spelling and the Irish spelling is not true? No, not at all. I have some church friends, who trace back to England, and their name is "Dawdy." But, as I say, it's more complicated than that.