Divorce is not a new invention (I have an ancestor who was divorced in the 1600s!), although it's far more common now than it used to be.
Particularly because divorce was unusual in the 1800s, the details probably would have been documented in court records of the jurisdiction where the divorce was granted. (Would that be Stafford County, Kansas?) I would think that you would need to inquire at the courthouse(s) in the place(s) where the divorce might have occurred.