David were there actually "Family Courts" back in the late 50's early 60's. I don't recall that there was.
Some jurisdictions yes (well you say 50's, I don't go back that far--as I recall the separate court rules started appearing in the 60's but it was an evolving process); other jurisdictions, the Court of Record "sitting as a family court"; still other variations.
Further, the Local Rules about what you needed to do in various kinds of family proceedings were sometimes separate and sometimes part of the Local Rules for the record court.
And one of the common things that did happen regularly was that the court of record didn't always do what the local rules called for in various settings. That was one reason given for the idea that we ought to have at least one judge who did divorce and adoption because that way we can make it happen in a fashion that gets stuff in the record on a reasonable basis.
This is not my area of practice but I am the lawyer for the real client so when an executive officer of my construction company client want's to do an adoption, I show up with the partner or associate who did the work; and before I show up, I real the papers and the rules so I have some idea what I am talking about.