I do not know about your custody agreement, how often your son is with his father and the girlfriend. Also, I agree with RoseBee's questions, how does your son feel, have you talked to him? For all you know, your son may have asked her to be involved or he may know of conversations between your ex and his girlfriend about him?

I would get as much surrounding information as I could before I judged the woman too harshly. Even with kids I wouldn't join the PTA and making the cupcakes that often? That's someone with different interests than I have but that does not make her bad in some way or better than me, etc. My husband's ex-wife is into cake decorating and kitschy stuff and so her behavior is lots different around the sons/grandchildren than mine is.

If she hasn't any other children to be around and enjoys your son for whatever reason, and wants to be part of his life/the family (if they marry, she will be part of the family and, if she has children, your son will sometimes be a part of that larger family when you are not) I would view that somewhat positively as it could make any marriage/life transitions by either you or ex, easier.