Oh dear, what a difficult situation. I think that lots of posters here have given answers and suggestions illustrating different points of view, that you hopefully have found helpful.
I think, putting a different view on it all, that if I discovered that my mother was talking to a ‘long lost’ niece (which you are in many way, as you stayed away from your aunt while her unpleasant husband was around) and was being advised about health and finances that I would be pleased that my mum had someone to talk to and confide in BUT possibly also be somewhat surprised, a little hurt and possibly a bit guilty that I hadn’t been able to provide advice for my own mother.
If your cousin was advising your mother for four years about health and money how would you feel? Particularly if you hadn’t known for four years?
My great aunt was 104 when she died, at home peacefully, and my mother was her surrogate daughter, visiting and staying as often as she could, while living two hours away. We also got on well with her and visited fairly frequently. We were quite shocked when we found out that a great great niece from my aunts estranged family, who lived five hours away, was also visiting for the final year of her life. Had we known, we could have organised visits better so that visits were better spaced out.
Hope it goes well and do keep visiting your aunt, lovely for you both. I can’t give any advice apart from that but I do wonder if Power of Attorney is a huge step to take at present? ?