A question that about divorce rates that comes up over and over is the extent to which making it legally harder or easier to get a divorce influences what people do. The biggest problem is untangling changing views about divorce from the legal changes. Often these are happening simultaneously so it is unclear what is causing the change.
There have been a couple of good papers from Europe that address these issues.
See: The Effect of Divorce Laws on Divorce Rates in Europe by Libertad González &
Tarja K. Viitanen.