Good to see that you and your kiddo are in therapy. How's that going? What's your therapist saying?
Sometimes in these situations, when we become the needy, do-anything-for-you-even-though-you're-a-jerk spouse ---- the attraction to us wanes, because well... .it's unattractive to be needy and desperate.

I think sometimes we look too far down the road to live in the moment. We get all wrapped up in the emotions (and the fear) that we can't see the reality of the situation. You're married (right now) and she's got one foot out the door. You haven't had sex in years and she says that's what she wants.
What are your expectations at this point? Right now?
Are they possible?
Not all people are BPD, not all people cheat, not all BPD people cheat, and those who cheat are not all BPD. Catch my drift? It's just something humans do. There's not a cookie cutter way to deal with a spouse wanting to stray in a marriage. It's also a symptom of a dwindling marriage, not necessarily a symptom of the person cheating.
My marriage survived fidelity. The best advice my therapist gave me was to stop being so pathetic and sad. It's part of what drove my husband to the arms of another person. I was angry, vengeful, bitter, upset, crying, whiny and did I mention angry? It made his mistress look like the much better choice.

I wonder if you were to back off a little? Maybe not take her so seriously (since her threats are idle anyways)? What might that entail?
Focus on you a little bit. On your relationship with your 4 year old. A hobby even - something that made you smile.
Do you think she would miss you?
Would your stopping putting the pressure on her help or hurt your situation?