From your first paragraph it's clear that he believes cleaning is your job and doesn't have enough respect for you or over-values himself to not bother to do any cleaning by himself. I don't think you should do no cleaning and have him do all of it to experience what it is like because he won't let you relax. Eventually he would perform the cleaning chores of the house that you do but it's a gamble whether he'll show more respect. Instead, it would be better if you two equally divide the cleaning chores. Once he becomes more understanding and respectful, each subsequent Saturday won't be a hassle, you'll both know what has to be done without question.

From your second paragraph I find myself to be in the same boat as Shezbut. It's difficult to understand whether some of your post are direct quotes or presumptions. It's also difficult to understand whether they were all uttered by you or a combination of your husband and you. Since I cannot parse that section of your post, I cannot answer all of the questions you posed.