I'm a 60 something woman, sounds like I'm in similar shape as your mother. I used buses and a few planes for a pleasant trip both North and South Island. 6 weeks, 15 hotels, I think. I had already been to Milford and Doubtful Sounds, so that wasn't included (add another week). This included a week tour to Abel Tasman (kayak, hike or use the shuttle boat between lodging), and a week in Dunedin. Most stops a minimum of 4 nights.
For shorter trips, just pick one or two bases and drive from there. You really can't go wrong with any base, there's loads to do everywhere. And with a base, you could go off on something more adventurous for a day or part of a day while your mom does something less strenuous.
Personally, I'd go for overnight on Milford and Doubtful Sounds, with a night in Te Anau between (check out Real Journeys), some time in Queenstown, and check out the glaciers. If you have more time, over to Christchurch on the train, and up to Kaikura for whale watching, swimming with the dolphins (your mom can be a passenger while you swim) and albatross tours. If Kaikura is recovered from the last earthquake. Even more time? Then up to Marlborough for the wine country and to Nelson for the Abel Tasman National Park. 5 day tours in the park including food and accommodations are available. Kayak, hike or take a shuttle boat between. I made it, so maybe your mom can, too. The hike was a bit more than I expected, though. Check carefully.
This, of course, is the South Island. On the North Island, I'd spend my time north of Auckland, up by Paia, the Coromandel Penninsula, and Rotorua if I had limited time.