I live in a four bedroom home with a huge yard. The secret is to clean as you go about your life. If you leave a room, look around, see if there is something you should take with you. Do dishes while you are waiting for something to cook. Buy a cordless vacuum for quick access. When the weekend comes around your house is already clean.

How do I teach the others in my family to do this? I've tried for years but they still resist or are incapable of it!

I'll let you know when I have kids. I did teach my dog to pick up her toys though.

Also, the less stuff you own, the less stuff you have to organize/dust/hide.

An alternative to not cooking is to enjoy cooking. I look forward to cooking, and enjoy the time I spend prepping for me and my partner, so I don't count it as housework.

Cleanup definitely counts though.

I have occasionally gotten sad when my wife was like "let's just order a pizza" and I wanted to cook something. Admittedly the cleanup sucks, but putting effort into something, completing it and then almost immediately getting positive(usually) feedback is sometimes rare, and can be incredibly rewarding. And that's just from an analytic perspective!