In a good marriage two people function a lot like an image of two hands clasped together. It is hard to see where one hand ends and the other begins. However, in this case, mistrust and infidelity has come between the "hands" of marriage. There is no longer unity and the relationship is faltering.
As you discover more and more about your wife's actions the hurt, resentment and anger mounts. That is natural and expected. She is apparently not at a place where she feels she can be truthful, yet that is what will be needed to restore trust.
Talking about this is indeed what is needed, but infidelity is such a powerful thing, (sexual, emotional or in any manner) that a professional intervention is often the only way to sort out, safely, what needs to be said. When we try to work out issues of this magnitude on our own it often results in polarized discussions where couples fight and have conflict. Not only do the problems not get resolved, but they often become worse.
I would advise against approaching this by yourselves. As you want to save the relationship for your child, the best practice is seeing a couples counselor.
That said, this is something that you can initiate even if she is not willing to go at first.
Although that may seem an odd approach, the best way to begin this process is for you to realize what you feel and think, and a therapist can help you prepare that process.
Be also aware that within the field of counseling, couples work is the greatest "art" within the field (it is very difficult and only the best can do it.) and this way it will also let you know, if you start solo, if the counselor has the talent and skills to help. Simply it is better you find that out on your own, than have a less than perfect experience with your wife present...
How can you trust her again? You can eventually but certainly not yet; she is not ready to commit to enough truth and discussion that it would make you feel she is through with this affair. You also are still very stung and injured by all this. The goal now is to allow you to express your feelings and thoughts to her in a constructive way and to encourage her to do the same. Trust will come back, but that is the end stage of counseling and you still have a ways to go.
This can resolve, but based on what you have said this does need a professional intervention. (Often your family doctor is an excellent resource for couples counselors as are local churches, who often receive these requests. Steven