First of all, let me say that I'm sorry you are having to deal with the very heartbreaking side of humanity. You are on the right track, though, since you aren't just smacking the "divorce" button in an attempt to bail from the stress of emotion. Right now you may be feeling lots of emotions such as rejection, anger, hurt, shock, disappointment, confusion, determination, and even apathy. Seeking counsel and talking about it instead of thinking "I'm too ashamed and God is powerful enough to help me in this" is best. While God is powerful enough to heal both you and your wife in the years to come, God also made allowance for a man to seek spiritual guidance from his pastor and elders in the church. Your wife, while confessing, is not ready to confess to the elders in her church simply because she isn't ready to give up the sin yet. She's not ready to answer for her sin either and is relying on you to baby her out of love. That speaks highly of you, btw, that she addressed the issue with you. It was in some ways a selfish move on her part, because she is trying to ease her guilty conscience. Never stop praying that God will turn her heart and mind to godliness and determination so she can let go of the sin completely.
Your job as the husband is really really REALLY hard, because you are supposed to help lead her in the family decisions. Part of this will have to be in the form of instruction. She can't continue in positions of ministry while she's hiding such sin, so the best thing to do is to seek the guidance from the leadership of the church. She can't just say "I'm too embarrassed to talk about it." Obviously SOMEBODY knows about her infidelity and she didn't seem to be too embarrassed then. Why should the loving (I'm assuming your church leadership is loving and not a bunch of fire-breathing dragons) church leadership she trusts to teach her family suddenly be inadequate to deal with the discussion about her actions as a parent in your family? At some point she's going to have to be told not to drag her heals. She's going to have to sink or swim and admit that she needs help.
In the mean time you, the man, may feel justified to lash out- be it in anger or through similar action. Keeping in consistent contact with the church leadership and strong Christian friends will also help with your accountability. Whether you and your wife continue to be intimate at this time is up to you... and the only thing the Bible really says about it is that the two of you can abstain from sex for the purpose of prayer and fasting for a SPECIFIC length of time. Basically, the Bible instructs that you be husband and wife unless you are abstaining to show God honor. God would lead you in that regard. If, however, you decide you want to pursue your wife and woo her back, Please don't consider it grovelling. Every woman deserves to be dated by her husband all through marriage, so get creative.
You can be totally in love with your wife and go nuts with creativity while still remaining within the boundaries God has delineated (and He doesn't give many boundaries for marriage).
Your wife, on the other hand, needs to be held accountable. She's not a child and you can't lock her in her room in an attempt to starve her vices, so addressing her obvious free time and lack of accountability is going to be a hard nut to crack. She's either going to repent and acquiesce, or she's going to buck under the pressure of consequences she will invariably have to be saddled with. All I can say is that I grieve a little for your both, because it is one of the most regrettable situations.
The Bible instructs that we admonish a brother to repent. It is very specific regarding the methods to be used in an attempt to help a brother take the right steps. It is also very clear what to do if a spouse asks to leave. Keep reading and praying and talking... and let yourself grieve.
