Re: jealous wife is cramping my teaching style
It sounds like your wife is jealous of this student. If you've ever been jealous, jealousy is a very painful emotion. It's too bad the student might have to suffer for something that has nothing to do with her. As a woman, I'm sure your wife would not want to see another woman treated unfairly. I don't think forcing the student to leave sounds very ethical at all. If she did have to leave because of this, I think you should be up front with her. Maybe she already has a boyfriend?
Definitely not shaking hands after class with students is a good idea. It must be difficult for your wife, thinking about how you might like this student better than her. It sounds like she is threatened by her. Maybe calling your wife immediately after class will help her realize that you're not interested in this student. Make sure your wife knows she comes first, and hopefully you won't have to quit teaching.