Re: vacuuming when you are physically unable.
I strongly recommend an iRobot vacuum cleaner (roomba). It will vacuum for you.
By the sound of it, your carpet is badly ingrained with dirt, so the vacuum will not get it all out in one day - but if you set it to vacuum every day (which few humans would normally do voluntarily, but the roomba doesn't mind) it is highly likely that over time it will improve until "clean" it a normal state for it.
Another benefit: Having a robo-vacuum on a schedule forces you to get in the habit of picking objects (papers, clothing) up off the floor.
But pets, smoking, and moldy clothes? Ick. A robot vacuum isn't going to put a dent in that.
pthalo: Think of your pets. They probably don't enjoy living in that environment. You owe it to them to make your home pleasant.
An exercise:
Name something that you do not do but should/wish you did/are told you ought, or that you do less than is normally recommended. (For instance, "exercise" or "eat vegetables".)
Make an exhaustive list of your sufficient conditions for avoiding this thing. (If you suspect that your list may be non-exhaustive, mention that in your comment.)
Precommit that: If someone comes up with a way to do the thing which doesn't have any of your listed problems, you will at least try it. It counts if you come up with this response yourself upon making your list.
(Based on: Is That Your True Rejection?)
Edit to add: Kindly stick to the spirit of the exercise; if you have no advice in line with the exercise, this is not the place to offer it. Do not drift into confrontational or abusive demands that people adjust their restrictions to suit your cached suggestion, and do not offer unsolicited other-optimizing.
To alleviate crowding, Armok_GoB has created a second thread for this challenge.