In the heyday of the stay-at-home mom in the fifties
First, it's not true that more detergent in your mop bucket or in your washing machine is better. This is something that my mother used to tell me all the time. You should only ever use the amount of detergent that is prescribed on the bottle for any given task. This will ensure that you don't have to do extra scrubbing. It also eliminates the potential for a film to develop on your clothes or floor from not having been properly cleaned.
It might be because of the overuse of detergent on the floors that my grandmother always told me to rinse the floors after I cleaned them or used a floor polisher. This was to ensure that the film I mentioned previously didn't develop and cause slipping accidents or disgusting residue. Even when using the proper amount of older cleaning products, a rinse was still necessary because their cleaning technology didn't allow for the product to dry and evaporate like those of today. It's not necessary to do an extra rinse on the floor with most modern cleaning products but you should still check the label on the bottle.
Possibly the biggest myth is that vacuums are only used for floors. Even if you have an upright vacuum cleaner, the vacuum accessories that are used these days can clean everything from carpets and hardwoods to ceiling fans, curtains, upholstery, and even cabinetry!
You should listen to the advice of those who are older and wiser than you but there's no reason to use outdated information to clean your home. Yes, you still need to dust before you use your small vacuum cleaner but otherwise you should strike out on your own. Buy yourself the best vacuum cleaner possible and clean in an updated way. Make new rules for cleaning but don't get too attached to them; they're going to change in a few years anyway!