You've confused me now too with the second part of your post relating to your Mums insurance.
Regarding the use of NCD it can only be used on one car at a time. There are companies that will duplicate your NCD onto another car, if you hold both policies with the same companies, but that is down to individual companies.
With your Mums insurance are you saying she insures your car with you on as a named driver and has two years NCD?
If you are then yes, if you sell your car and buy another and your Mum is insuring that one, her 2 years NCD will be valid for that new car.
Hope this helps!
