Bearing in mind that the America you're probably talking about started in 1776, the worst part of America's history would be around 90 years later.
You know, "Four score and ten years ago this nation..."
You were in the middle of a civil war. It was often a war of brother against brother from the same family, village or hamlet. It was a bitter, no-holds barred war in which more Americans died than in WW1 or WW2 and Korea and Vietnam combined.
We've seen civil wars in many nations, and they continue, such as in Syria at the very moment. All wars are abominable, but civil war is probably the worst of all.
So in answer to your question: The American Civil War of the 19th Century.