I don't know if what I have to say will really help or not but I have a similar story. My husband's grandmother was always right on top of everything and never missed a beat. As she got older, she started second guessing everything to the point of downright paranoia, like what is happening with your mom. She was determined that certain things were going on like doctor's lying to her about things or that her adult children were getting into her financial information behind her back or that people were taking things from her home. Even if she said, so and so stole that figurine and I know they have it and I want it back! And then we would show her where it was, sitting on the shelf or whatever proving that noone stole anything from her, but that wasn't good enough because that just meant that whoever she was accusing got wise of her and put it back when she wasn't looking. The older she got, the more out of it she seemed. She recently passed away, she was 85 and died of natural causes. But, even though we couldn't get her to take the mood medications her doctor prescribed her WHEN we could get her to go to a doctors, and even though I know you can't force someone to do something if they aren't going to do it, I've always felt guilty that I should've done more. I know that doesn't help, but I just wanted to let you know that you're not alone.
The only thing I can suggest is to do whatever it takes to get her to a doctor's office even if it means lying to your dad about it. There is help to be had. But remember not to beat yourself up if you can't fix this. Do what you can but realize that you can only do so much. Most importantly, humor her and be supportive to her and don't let her see you get frustrated. It sounds like your dad doesn't understand and like most people from that era, don't really want to. So, she needs your support and your help to get through whatever she's going through. Just remember that with as much support and help you give her, ultimately, it will come down to her choice of accepting it and that's something you'll have to come to terms with. Trust me, I know that's hard! But, you can only do what you can.
Oiy - I feel like what I've written probably won't help at all and I'm sorry for that. It's so hard to know wha