I don’t know what to say. This has not been my experience. It was certainly true of my parents’ and grandparents’ generations. In their cases, the wives did not work outside of the home. I had a career and raised a child. I did not do the second shift you refer to. I am now retired and my husband, who still works, does more housework than I do. I do all the cooking because I love cooking. None of my friends who are my age have ever complained about this supposed second shift, even when they had 2 or 3 children. All the men I know under the age of 80 do their fair share of housework.
Maybe the people I know are atypical.