So you're ready to go from inviting her to stay for dinner so she doesn't feel like hired help, assuming she'll politely exit stage left, to "nothing gets the message across like the cops showing up"?
You REALLY do need to work on your communication skills. Not your wife's, not the girlfriend's, but YOURS. There are more than those two extremes. That's no way to handle this.
I hope you learn and grow from this episode in your life, that is all.