D.B.
I would un-friend her, and have your husband do it too. Even if you take the whole jealousy thing out of the picture, he needs to protect his professional associations, and her photos/behavior aren't helping him. He can say (and you can say) that the photos are a bit much for someone you met professionally and will occasionally see in a professional setting, and are obviously meant for her true good friends only.
He needs to step up and, rather than make jokes about how hard it is to be married to him, just stare at her blankly when she is cozying up to him. He may need to say straight up, "You know, this is a professional networking event (conference, lecture) and it's essential for everyone's careers that all behavior be strictly business-like." Then he needs to excuse himself and say, "Oh, there's Joe. I need to connect with him." Then he moves to another circle of professionals. He should absolutely sit with a different table at any luncheons. I know he doesn't want to be rude, but she is not helping his career, and he's not helping his own by being charming.
You say she's not doing anything wrong. But she is. She's being unprofessional.
You don't have to be so careful - you are not making 'friends' with your husband's professional contacts. I would say so, and suggest to her that she is in these classes to advance her career, not to be friends with people's families, and you don't think you have any professional contacts that can help her. You might suggest that she use Linked In rather than Facebook for professional contacts, but do not let your husband connect with her on LI either. It's going to hurt him professionally.
In time, she will move on to another target, and your husband's professional reputation will remain intact.