The same old pattern ... I am sad to read about it. Chipmunk is childish and pouty, Airyn is indecisive and you are stating your boundaries but start to act for him as soon as he isn't able to uphold them himself.
I can understand that she is unable to respect you and your relationship but simply because he isn't able to do so first. The problem is definitely Airyn but mainly because he doesn't want to end the relationship. That seems to be a fact he tends to omit when necessary and you don't want to see. You can state "I won't be tolerating her in my life' as much as you want, Airyn isn't a partner who is able to keep his relationships separate to that degree. You on the other side, leave a minimal space in his life for another relationship, which is your right, you state what you need, but she will never be satisfied with that. And the saddest thing is: Each and everyone of you knows this. You are hurting each other unnecessarily, someone needs to step back.
I hope that this comes to an end soon and you find some peace.
Facts: 30, female, bi, v-type relationship with Sward (husband, straight, mono) and Lin (boyfriend, straight, mono), poly-fi and co-primary.