Copenhagen tends to be a town that is best approached via foot or public transportation, but it is very flat and transportation is all very accessible.
Given that most sights do involve walking (i.e. through museums, castles, gardens, along streets), you might want to peruse the guidebooks and pick a few main places to visit, and then have some extras if your mom is up to it. You can divide the days by location - perhaps one day by the main station and one by Nyhavn.
Then perhaps you can 'do' one thing in the morning, and have a nice long lunch and a relaxing afternoon, for instance people/boat watching from a bench down by the harbor or in one of the gardens. Some places must be done on tour in one shot, but many can be done at leisure, with time to sit down and enjoy the scenery and have a lunch or snacks. Getting a good early start might be helpful, as crowds can be energy sapping.
Also, a harbour tour might be a nice, low energy way to see the city.