https://www.youtube.com/watch?v=-ot7amDyqbY
This seems to be a Confederate song, judging by its text. But when you look up "The Irish Brigade," it's part of the Union Army. It also mentions Patrick Kelly, who was an Irish-American Union Army officer during the American Civil War.
Can somebody clear it up for me? Thanks.
This site attempts to lay out the stats for Irish immigrants on both sides of the conflict. Exact figures can be disputed, but it is clear that the majority fought for the Union. Besides the numerical weight of the story, the Fighting 69th and famed exploits of Irish Federal soldiers, in general, made those on the Union side more famous.
After the war, it was also natural for immigrants to boast of fighting for the Union, since that side won. Celebrating being on the losing side came much later.
It is indeed a Confederate song, and your confusion arises from the fact that it does not mention Patrick Kelly, but Joseph Kelly, a pro-Confederate militia officer in Missouri before the war. He later became a Confederate colonel, commanding a regiment of the secessionist Missouri State Guard and then serving as a staff officer in the Trans-Mississippi Theater. The "brigade" in question seems to have been Kelly's 1st Rifle Regiment of the Missouri State Guard.