It doesn't sound like your boyfriend is deliberately trying to hurt you, but that he doesn't know how to cope with this situation.
On one hand, you say she cannot communicate openly with you. On the other hand, you call her an abusive liar and manipulator. How much direct contact have you had with her? Is your impression based on the information that filters through your boyfriend? Is it possible he's just doing a really crummy job of being the go-between, and both your messages are getting muddied up? That's always a difficult position for anyone, since it requires him to have an impossibly perfect understanding of how you both feel.
Is it possible you have the same inability to communicate openly with her? It sounds like you weren't even talking to your boyfriend about how you felt, until it all came pouring out in an angry letter. Letters like that can be therapeutic to write, but are sometimes best left in a dresser drawer. I read somewhere that Mark Twain used to write very angry letters to all kinds of people: politicians, editors, businessmen... but his wife would always tuck them away instead of sending them, knowing the harm they would cause to his relationships with these important people.
I wonder if his parents got the whole story. After all, most people aren't very progressive about poly and would see his actions as cheating, especially since he is violating boundaries that you both agreed to and so is, in your mind, cheating. If all they know is your angry letter, they may not fully appreciate the situation.
You have every right to be upset that they were making life-changing plans behind your back, such as moving her into your home. However, it doesn't sound like she's going anywhere any time soon. That leaves you with a couple choices. Clearly the status quo is out.
Of course one choice is to throw in the towel. Another is to request that the three of you sit down with the kink-friendly counsellor together and work things out. A good therapist can really facilitate communication, and having an "audience" can help you all tame your emotional reactions as well as rephrase things that you struggle to express. This type of setting can create a safe place for her to communicate. Even if she doesn't come, at least you and your boyfriend going together will help the two of you develop communication skills that seem to be lacking. It's really promising that he is willing to see a counsellor to help fix this relationship. That shows that he's invested in you and cares about how this turns out.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker