Ree - I have to start by saying, I can understand how you would feel that this is a really messed up situation for your son. You're defninitely fearful for him, and your posts imply that you want so badly to drag his little butt outta there and shake your finger at him and tell him to never do that again.
Your son is 24. Not 4, not 14....24. What does this mean for you, his mother? It means you're finished raising him, and you're finished paddling his bottom for mistakes. It means you're no longer responsible for him. It means you have to let this go, because quite honestly, its none of your business. I completely agree its twisted, (it's terribly twisted), and it has potential to get even worse. I totally get it and agree with you there...but in the end it's still none of your business.
And to reject her automatically based on hearsay, without even meeting her or wanting to...you have already shut the door and you don't even realize it yet. Be honest with yourself...what CAN you do about this??? Can you really stop it? Do you even have a right to? What if your son does marry this woman? What if he does have a child with her? Are you going to refuse her then, without at least giving her a face-to-face shot? How did you feel the last time someone did that to you?
I think you owe your son that, you at least need to meet her. He wants you to know her and approve of her, thus he's asked you twice to meet her, according to your posts. You have predetermined notions of her and you have already formed an opinion of her and you haven't even met her. That is sad, and it is dangerous territory my friend. Also know that if you deny her, you are denying her children...even those potential future chilren that might belong to your son. I know that's a scary thing to think about, but I can tell you as a DIL that anyone who can't treat me at least civil does not get access to my children and I'm sure you felt the same way when you were a young mother. And chances are,too, that if you deny her, your son will eventually resent you for it (IF he chooses to move forward with that relationship), and then you may have to say goodbye to him too. So put that on the back burner....it could happen. And your actions today can determine the outcome of any future relations you have with her AND your son. I would tread lightly.
Creme offers some very sound advice....you can tell him to "trust his intuition." It's neutral, its safe, it devoids you of any guilt. He's an adult, and if you raised him right to the best of your ability, then you have to trust him to make the right decisions for himself, even if they are not the decisions YOU would make for him.
That being said, I hope this works out. It is a terribly twisted situation that could get worse for your son. I hope it all works out, and I will pray for PEACE for you.