It was not that simple, and many generations past.
Long before we were Burned out of Alabama during Reconstruction after the last Civil War.
Well yeah it that simple and you explained it with "many generations past". Somewhere waaaaaay back in your family tree a pure breed Scot ancestor married a pure bred 'Mick'. I'm 1/2 Irish so I can say that ;-)
And it makes perfect sense that your family goes back to Alabama as if my history is correct (it is), the South was mostly settled by the "Scotch/Irish", though usually a bit further North.
And not to hijack the thread but when I see "Reconstruction" I get sick (I'm from IL and my family tree always was 'Northern'). That time is a stain on the USA. The repercussions of that affected Southern Whites for almost One Hundred years and kept the South poor as pi$$.Over the years I've had friends and neighbors from Georgia, Tennessee, Kentucky and met & talked folks from West Virginia and Northern Florida (it Ain't Disneyworld). When I heard what they had to do to scrape by, I got just as mad at the 'Yankees' as they were. Not until recent times with factories moving South to escape unions has the South had any real chances financial growth.
Anyway, have a Happy New Year :-)