I think the response misses the point: LW's complaint isn't about having to do the housework, or about how to teach the kid how to do the housework – it's about how to teach the kid "As a human being who lives in a household, you are reasonably expected to (a) clean up your own messes and (b) pitch in with general household tasks," when Mom...doesn't.
So LW does 100% of the traditional (cleaning, etc.) housework. Is there anything Mom does 100% of? If not, is there anything related to household responsibilities that Mom could do 100% of? Then when the kid complains, "Why do I have to do housework when Mom doesn't?" LW could say, "Well, you and I do all the housework, but Mom does 100% of [thing]." Sure, that's not the real justification for Mom doing no cleaning, but it could help underline to the kid that everyone has to contribute to the running of the household.
no subject
So LW does 100% of the traditional (cleaning, etc.) housework. Is there anything Mom does 100% of? If not, is there anything related to household responsibilities that Mom could do 100% of? Then when the kid complains, "Why do I have to do housework when Mom doesn't?" LW could say, "Well, you and I do all the housework, but Mom does 100% of [thing]." Sure, that's not the real justification for Mom doing no cleaning, but it could help underline to the kid that everyone has to contribute to the running of the household.