@Dredcor the one I referenced was entitled "The National Survey of Families and Households" in 2011, and there is another onr that I know of from 2019 called "Life Course, Generstion and Gender," though I'm less knowledgeable about their pedigree given it's Norweigan.
Now, one could cite a study from Cambridge about how men are happier when sharing housework as a rebuttal, but there are also plenty of explanations for that (for instance, the common idea that wives nag a lot and that a happy wife makes for a happy life). I don't know that sharing housework has a higher correlation with divorce, anyway, just that unemployed men are divorced more often than employed men, so I wouldn't consider it a rebuttal as much as a point of interest that should be explored.