My mom gets about three hours of sleep a night. She's always so tired and dreary. She insists on wiping down everything every night (not just cloth and water), mopping all the floors, dusting, etc. It's an obsession with her really. I've tried helping more around. Did the dishes, helped her wipe down all the counters, mopped the floors, but she has to redo everything because she doesn't trust that anyone else does it well enough. My dad's tried to help more with the cleaning (but he comes home quite late from work everynight) but it's the same thing, my mom has to redo everything. Thing is, our house is always really clean even when it's "dirty" in her mind. As a result she will go to bed around 3 or 4AM and has to wake 6 or 7 AM.
It is an obsessive-compulsive disorder concerning germs. I used to allow many things concerning the cleanliness of my household, but one day I realized that life is too short to worry about this obsession! Who cares if the husband comes in with mud in his boots, tracking it from the door to where he finally ends up?! I would rather spend time with him than being angry at him for being so insensitive! He would clean up what he could and when he's gone back to work, I'd clean up then. Now, all my floors are tile and hardwood, so easy to clean. Just keep letting your mom know that life is too short to worry over little things. What matters is in the heart! Good luck!
Sorry that this isn't an answer but more of a comment but i am just like your mum.. with my room especially. Its true that being in a clean environment helps you feel relaxed and actually happier.. she is in a routine and she doesn't realize there is anything wrong with it. Best thing to do is slowly break her routine. She isnt bothered about how clean it is she is just used to the cleaning.
Your mom is germaphobic. Ive heard that that's the easiest case of phobia/OCD to cure though. Look it up online and suggest that she get some therapeutic help because this is infterfering with her life as well as yours and her family's lives.