My father had a stroke a year ago. He stumbles and stuffers and forgets. My mother stopped taking her meds. They are stubborn and won't use a walker or cane. My mom doesn't go to the doctor anymore. She goes into fits when we talk to her to do certain things.
When you ask mom to do certain things and she gets angry, is her behavior reasonable? If not, I'd ask why. People who don't take their medications can develop medical and mental problems. I'd insist that she explore why she's not taking care of herself and dad. If she still resist seeing her doctor, taking meds, and it' results in her neglecting dad's needs, then, I'd have to step in.
Are you their POA? I'd see an attorney to get legal advice regarding dad's care. Regardless, I would not stand by and let dad suffer from lack of care. I'd let her know that politely, but firmly. I'd be my dad's advocate and make sure he's properly taken care of, whatever it takes, though, I wouldn't relish going to court about it.
I used to think that my LO was stubborn because she wouldn't use her cane or walker, but, then I discovered that she merely could not remember to use it. That could be the case. If so, then they have to under supervision so that they can be reminded to use their cane or walker.
I might try to spend several days around the clock with them and observe how they are really functioning, so you have an accurate picture of their actual abilities. I don't think that pleading, convincing, threatening will help the matter. Most seniors don't respond to it and if they both have mental decline, they wouldn't respond to it either.
I hope you can get some answers and that something works.