I don't recall doing much grocery shopping with my mother. She must've done it while we were in school, but we always had good food in stock. When I got my license, she sent me out for piddly stuff. (I begged to drive and it was very convenient for her.) So I can't say I learned how to plan menus, but I did learn to "hunt and gather" from her. I also learned that feeding one's family can be a joy. Her motto was, "If you're going to have to do it every day for the rest of your life, you might as well enjoy it."
Mama taught us how to clean the bathroom when we turned nine. It was a sort of rite of passage. Not that any of our friends were jealous to join in the ceremony or anything.
She was meticulous about laundry, sorting all the clothes by color, weight, and fabric content. She never stuffed the washing machine, which I think is the reason that her machine, which she bought used in 1972, lasted over 30 years. I don't do laundry the same way, but I learned how not to ruin clothes, and was prepared for living on my own by age 18. The thing she still loves about doing Daddy's laundry after 47 years of marriage is that Daddy is still alive to dirty it. And Daddy, bless his heart, positively beams when he sees a drawer full of clean underwear, all folded in crisp right angles, courtesy of his bride.
I'm curious what you other ladies learned from your mothers in terms of homekeeping. What "stuck" with you, and what methods have you altered, for good or ill?