If you know the state and county, you might be able to get it by writing the county clerk and only have to pay copy fees.
The divorce should list all the minor children and their custody, property settlement, cause of divorce, etc.
Not all early divorces were for adultery or abandonment. There were some for brutality, failure to provide and a whole host of reasons.
In many states, divorce records are completely open public records like any other civil court action and can be obtained by anyone.