Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
Your wife betrayed her vows to you. That part is easy to understand. She could have come to you if there were problems in the marriage and talked to you. She didn't. Choosing to cheat does not mean the marriage was bad or the betrayed spouse was a bad husband. It's more to do with the morals of the cheater than anything else.
Telling you that you are failure as the spiritual leader of your family is unfair. Your job as leader is to lead, if you have been given that role. Her job was to follow, if that was the role she accepted. Remember the old saying, you can lead a horse to water but you can't make it drink. I think that applies here.
Your wife needs to work with a good therapist on her character issues. If you just continue on with her without truly resolving this, then she may fall again. You owe it to yourself and her to lead in the right direction. I'd ask her to make an appointment and have at least one visit together before she starts on her journey of self improvement.
If your value your spirituality, I would consider this a test of faith for you. Maybe it's time to reevaluate if your particular denomination is the best choice for you and your family.
Ask yourself the age old question of which is more likely to get you into the gates of heaven:
Blind faith that is never questioned from cradle to death, with your blindly following the way you were taught without questioning it.
Or questioning everything you believe in, seeking guidance from God, and being open to him leading you in a slightly different direction.
In other words does religion mean more when you question it, seek knowledge, and rededicate yourself to your belief structure with open eyes?
There is no reason that this should even stay a secret as her crime is also against God and the church.
There is something call church discipline where she apologizes for her actions that have tainted not only your marriage but your church.
That being said the church members, while being disappointed in your wife, should help support the reconciliation of the marriage and the growth of your wife going forward.