She's not done with OM. The fact that she's willing to introduce your S to him and play "happy family" with him says that she's fantasizing about what life with him would be like.
Her promises to end contact so far don't mean much.
She's acting like a teenager right now, and when you make ultimatums, you come off looking like her father instead of her partner. If you tell her what to do, she will rebel and ignore you. Instead of making demands, next time it comes up, try telling her what your family needs to feel safe and protected from predators like OM.
