This isn't a polyamory problem; this is a dishonesty problem - and if I am reading your post correctly, not the first
Here is how I tend to look at such things: cheating sucks ass, but the person you had the relationship with when the cheating began was your husband; it was he that broke your agreements; not the other woman. The other woman may have substandard ethics, but at that point you had no agreements with her. That said, because of the long term relationship with your husband - the one who actually broke your agreement - you are willing to work things out with him, and shift much of your anger and blame to the woman with whom you have no history or agreements.
Why should she bear more of the blame and anger than your husband? Because she is a stranger and you have nothing to lose by maintaining your anger toward her rather than the one who actually broke your agreement?
I can't answer your question for you. It is obvious you are angry, and rightfully so. I would say that regardless of what you do, this anger needs to be put to rest. I would suggest that perhaps you and your husband need some counseling.
And I have to ask this question: if your husband cheated before with this woman, what is to say he won't again if you veto their relationship? Is that a good reason not to? No, it is not. Posing the question is to point out that there are larger issues here: your husband's inability to stand by his agreements. This kind of behavior does not work in monogamy or polyamory.
Last edited by bookbug; 11-23-2013 at 12:39 PM.