Not a parent, but I had this with the Elderly Person I Cared For (EPICF) over a period of about twenty years. I could have written your posts word for word.
I've posted a more detailed history before but with my EPICF it took about ten years for mild paranoia and delusion to progress to fortifying the flat with alarms and cameras, destroying documents, and hiding purses and money. She believed there was nothing wrong and refused to speak to the GP about it. At around about this time she started having auditory hallucinations - she could 'hear' relatives plotting to take her money and harm her which then started off vicious cycles of anxiety, panic attacks, shortness of breath and so on. She was prescribed anti-anxiety meds but refused to take them. She was still capable of functioning otherwise - activities of daily living were fine and she was in no danger to herself. She was an abosulute maestro at lying to health practitioners.
This went on another eight or nine years until after one particular episode social services got involved (she'd rung 999 several times to report items stolen from her flat) and then shortly after she agreed that her memory was failing and she was referred to the Memory Clinic, which is how services are accessed around here.
Her cognitive function was found to be very poor and the memory nurse felt it was classic dementia with Lewy bodies as with PP above, but the nurse was overruled by the consultant who, without seeing her, diagnosed late onset psychosis and prescribed medication for it. When it became obvious that she was refusing to take the medication they 'discharged' (washed their hands of) her.
The GP and social services made a further seven referrals back into Older Adults Mental Health services and they simply declined all seven referrals so we never got a diagnosis. By then she was in her mid-90s and her physical health had almost completely evaporated, and between several falls and trauma she just bounced in and out of A&E for several months. The NHS just pushed her back home saying it was social needs, while continuously referring to 'undiagnosed dementia'.
I wish I could offer you something helpful, if not positive, but I'm afraid I cannot. Push for a diagnosis any which way you can: NHS mental health services did not want to know once she finally couldn't run from it, and the last few years of her life were horrendous for her, and for me. Nine months after she died I'm still utterly broken by it.
She had driven away everyone around her. Distant relatives who phoned her once in a while stopped when they got a story about the late husband's nephew squatting in the ceiling or walls, sneaking in when she wasn't there. Social services regularly checked her for capacity which she maintained until about a year before she died. That helped with securing her banking arrangements (I had a LPA but she still had access to her money until she lost capacity) but didn't make a dent in the practical and emotional effort of dealing with the consequences.
All I would say is that I wouldn't refuse to hold POA. Sure, it can open you up to accusations of stealing, but you can protect yourself simply by keeping good records. If I hadn't done it and had lost control of my EPICF's finances I dread to think what could have happened.