If I were you, I'd nip it in the bud by putting on my best 'don't mess with me' voice and say, "H, we need to talk. It is completely unacceptable for you to speak with OW in my house. This is a very disrespectful thing to do in front of me and it is not okay. Under no circumstances are you to contact, speak with OW in, near, or around the house. Am I clear?! Thank you."
