Hey "D", how are you doing? It looks like you're feeling better. Give Colville a wave for me the next time through. One of these trips, I've GOT to stop by the Examiner office myself and do some lookups.
The 1930 Census shows Robert A. Hodgson, age 16 (1913/1914), in Owyhee County, living in Homedale, as nephew to homeowner Jesse L. Proud and his wife Anna. Also in the home is his brother(?) Joseph W. Hodgson, two cousins(?) also nephew to homeowner, Conrd M and Edward L. Sutton. Jesse's sister, Flora H. Walter is also in the home, but not enough information to identify if she is mother to any of the children.
Based on years of reviewing cases in my old career... This civil case "sounds" like a dissolution case. A divorce case is a civil matter in the court systems and is heard at the Superior Court level (Superior Court in WA State, District in Idaho, varies names in other States) in each county. It is "potentially" possible he had sued a sister/sister-in-law over a family estate or something else; but, I doubt that.
Court records are maintained in each State/County per law in almost all States (at least all the ones that I've had contact). These records are maintained in various manner. Recent cases are usually found on computer records by case name (Robert Hodgson vs Francis L Hodgson; sometimes in dissolution cases the "Petitioner" and "Respondent" names are also on the title). Older cases are maintained on microfilm and also in hardcopy, sometimes both. The Court Clerks of that court also have a "Big Book." This book, usually red in color, about 18" x 24" has a chronological listing of the case titles. Since you don't know the year, they would have to go through this book, listing by listing, if they don't have the entire case listings on computer (which I doubt).
Now, your case: If all you have is his name versus her name and the name of the county, it was "probably" heard in Owyhee County. But, as Petitioner, he could have filed in any county where he lived, against her in any county.
I did run his name and found a Robert A. Hodgson, approximate age 44, previous address Post Falls, in the database system: http://owyhee.idaho.staterecords.org/?uid=rmfcode&TID=T7...
The one listed in the 1930 Census would have been 44 in 1957/1958. If he married Darlene in 1959, this one is "possible." But, you DON'T want to pay $29.00 for the record.
I would suggest you call the clerk's office and ask them for their procedures for obtaining case information: http://www.owyheecounty.net/index1.php?court
Some clerk offices do the research, identify how many pages, how much, then notify you to send payment. Some require a payment form first (credit card). Some do not do it by mail. When I've requested records, it's been in person; but I've overheard them on the phone giving instructions, some require a personal visit and review of the case file. Some will photocopy the entire casefile, with all the individual filings. You don't need the entire case file w/all the filings. The original petition and the final declaration would be sufficient. Any child care/support, spousal support, would be identified in the final declaration.
I'd suggest contact with Wayne Hodgeson, or Gordon Caseman. As you wrote, it appears Gordon might have been the son of Francis. One of them, or other family member should know of a previous marriage. But, if for many reasons, you don't wish to do that, the above is your option. His wife, Darlene's, obit is online; however, you already have that also.