To answer your question - your judgemental family is the problem, not your cleaning. I have my own (pretty loose) cleaning standards, they don't apply to others. If someone invites me to their house, it would have to be pretty dirty before I might say something, and even then more because I might be worried about them.
We do kind of a lot of ongoing maintenance, run the Roomba twice a day and have help - we pay for every other week deep cleaning. But generally speaking yes there is cat hair and dust. We live in the world, the world is made of dirt.
Why is she mostly responsible? My husband has higher standards for housework than I do, so I do more of the cooking and gardening, finances, we arrange the division of labor to accommodate our strengths.