OK first of all, welcome to the forum.
Second of all: OUCH! Being cheated on and lied to like that is absolutely horrible - the betrayal of trust and the hurting that goes along with that.
Is she still determined to keep up a relationship with this third person while you work through this, or can there be a true break from it, to give you a "safe place" from which to work?
One thing that I feel is important in a situation like this in order for polyamory to stand any chance of working - you two needs to work on the trust thing - if you can't get to a point of trusting each other then you are going to make it very hard, or impossible to make polyamory work. I think that everything else is (relatively-speaking) details.
Right now I can imagine you are in a position where you feel betrayed and that you can't trust her - and those are valid feelings, given the fact that she has lied to you and broken the rules of your monogamous marriage. I believe strongly that trust has to be earned - in this case she is going to have to work to regain your trust.
Please feel free to talk more about what has happened since you have found this out - share as much or as little as you like.
Please check out The Birdcage - an open, friendly Polyamory forum for all parts of New York State
"Listen, or your tongue will make you deaf." - Native American Proverb