Arsene, if you feel uncomfortable having the friend over to practice, it's okay to say so. Your email to her sounds okay. She might be upset about it, but what can you do.
I see the OM as an escape. She's running away from something--her responsibilities as a mom/ W? Her past? Career frustrations? It's good she's opening up to you more. If you don't judge or criticize, or get offended, she'll open up even more.