@unsureofthis; There's a lot of issues that have to be worked on. I can't imagine trying to be involved in a polyamorous relationship where trust and honesty were not basic precepts.
It can be very hard in a situation like this. Your wife's new lover can be incredibly attractive (and I don't mean physically here). There's tons of NRE (new relationship euphoria) flying around. It's exciting, new, feels fantastic. There's no responsibility, no deep conversations about the love that is developing, just free and wonderful feelings.
Then there's you; right now, you're bringing concern, betrayal, sadness, a necessity to work on the relationship, the need for deep conversations.
It's incredibly hard to juxtapose those two sets of emotions and think "Yeah, I'll go with sadness for the win!" Your wife is in a very tough spot as well as you. Quell your anger, quell your (valid!) sense of betrayal. The way forward should include validation of your feelings but should not include anger from you towards her and doing things that tear her apart.
I'm aware of one couple where the husband came home to find his wife having sex with another man. When he came in the door, he could hear them going at it. They didn't know he was there yet. He had a choice to make; get angry, or join in. He chose the latter, and it has added immensely to their relationship. That's not to say that cheating is somehow a good thing. It isn't. That needs to be addressed and the fundamentals of your relationship have to return to solid ground. But, this doesn't have to be the end. It could be just a beginning on a new path.