@bdp24, I don't think watching "The Birth Of A Nation" will give you much insight about your relatives' beliefs. It's an adaptation of a book and play titled "The Clansman: An Historical Romance of the Ku Klux Klan". The film was instrumental in the nationwide resurgence of the KKK during the 1920s. The Stoneman family play a prominent role in the movie, but I don't know if they are linked to Stoneman's Calvary from the song.
I want to thank you for sharing details about your family. It's not always easy being the person you want to be. If you want to understand racism in American history you should start with "The 1619 Project". The same people who wrote that all men are created equal were enslavers. Go figure.
@mahler123, I agree with your description of the characters in the song, however, if you get into a war you have to win. And if that means killing woman, children and the elderly, then that's what you have to do. Read up on the bombing strategies of the Allies in WW2. The bombings of Hiroshima and Nagasaki are another good example of doing whatever is necessary to get your enemy to surrender. The moral high ground is to not start a war, but if war is forced upon then destroy the enemy by any means necessary.