For a moment, take this completely out of the polyamorous context. Because at this point, you are not polyamorous, you're just a guy having an affair. That's how your wife will see it, and that's how I see it.
Whether the mistress is poly or not is 100% irrelevant. Your wife will not give a hoot what the other woman's excuse or lifestyle is, she will blame you for stepping outside the marriage.
There's no way that your mistress should be the one to tell your wife about the affair.
I understand she's probably trying to be helpful, figuring she "knows about the lifestyle" and can help your wife understand.
But no good can come from your wife hearing that her husband is having an affair from the mouth of the Other Woman. Your wife will be hurt and probably angry. Having the mistress present the news will likely leave her feeling even more betrayed.
My other concern is with this woman calling herself poly, and yet having no reservations about beginning an affair with a married man. While being poly does not automatically make a person honest or good at choosing partners, it does give me a sense that she may not have very much experience in the lifestyle. For her to further offer to tell your wife that she's the mistress sends up big alarm bells.
“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