I am not a lawyer, but here's what I know.
Generally speaking, if they are married, the engagement ring was given to the soon to be wife in expectation of marriage. It sounds like that part happened.
So I think wife could keep it, cheating or not.
However, if she handed it over, that might be different.
I don't know how things are in West Virginia, and I could be wrong, but I doubt anyone cares if she was the village whore.
What makes you think she won't show up?
In my humble opinion, the woman cheated and gave back her engagement ring. If it were me, $4k would be a small price to pay to be done with her. I'd probably hand her the ring, get the divorce, and that's the end of her.
But that's just me.