Loads of sensible comments. I would like to add that you should address the stubbornness. Now its about stairs, but soon it will be about driving, or other contentious issue.
Speaking from experience, this requires persistence, might take a year++ to come round.
Very good point. Driving is a sticking point for many. With my mother it was basic time/energy management. She used to wear herself out doing stuff that provided little happiness to her or anyone else, especially around the holidays, and then be absolutely exhausted - or even in the hospital - when a bit of energy/wakefulness would have had more positive effect. It took many years of often-acrimonious discussions involving myself and my brother before she started managing those precious "spoons" more carefully, and by then it was only a couple of years before we lost her to dementia so my daughter barely got a chance to know her at all. It's not easy to be that forceful with one's parents, but sometimes it's necessary.
