OP I think what you have written about your cousin's past history is insightful and probably, as you suspect, holds the clue to all this. When my DH was unfaithful, it was important for me to understand the mindset of the person he'd got involved with.
This person seemed to have deep psychological issues. She never knew her Father, but despite this, grew up as a spoiled only child with her mother and grandparents, all of whom lived together. My DH says that it often amazed him how childish she was and how she felt the world revolved around her and that everyone would be interested in the absolute Minutiea of her life.
Even before she met her husband, she couldn't form strong friendships with women, because they sensed something in her - plus she seemed to define herself by how many men were lusting after her - even those in committed relationships. She managed to cause a lot of trouble for a lot of people and left every job under a cloud because she had caused so much mayhem.
She married a man who had at least two affairs. This seems to me to be the final bit of the jigsaw before she set her sights on my DH (having tried to get him years before). I think at that point, she was so damaged, that part of her agenda was to cause as much havoc as she could to a woman who seemed to have what she didn't - the husband she had always dreamed of, the children she couldn't have (allegedly, she had miscarried a few months before) and I genuinely believe this woman's agenda was as much about inflicting pain on other women as it was about having a relationship with my DH.
When he ended it with her, she even posted hateful attacks online about our 11 year old DD, FFS!! My DH's counsellor believes that this woman has always had a problem competing with other females and that this got worse once her H was unfaithful.
I'm sure your cousin isn't like this, but I DO think she feels she has been badly treated by men, is probably hugely envious of women who don't seem to have had that treatment and in some deep-seated way, doesn't see the harm in bringing pain to an innocent woman.
It takes a lot of moral courage to walk away from a real attraction, but walk away she must. She will get her reward for doing just that too - life always has a way of rewarding us for doing the right thing. The road ahead with this man is full of misery.
And for what it's worth, a bit of moral indignation on your part would be no bad thing. Too many people sit on the fence on these matters and fail to say that somethings are just plain wrong. If more people realised that they might just lose the support of people in their lives, if they continue to do a bad thing, I'm sure there would be more of a deterrent factor.