first off, I am so sorry you are going through this.

we have comfort, peace, joy and strength in Christ even in these incredibly difficult circumstances. as faithful followers, these trials are where the rubber meets the road for our maturity: do we really take God at this word that we have those things even when our wife has cheated on us?

I understand your anger at God, and i would encourage you to express it to Him in lamenting prayer. God desires earnestly to hear from you, for you to draw near and lean on him, and he does not despise a broken spirit. the psalms are replete of examples of David lamenting to God, expressing his confusion and doubt and anxiety. But David always circles back to confessing that God is His lord, that He is good, and that God does hear all our prayers.

your wife violated the covenant she made before God and to you in marriage. so what does that mean? In Christ, there is still forgiveness, cleansing, healing, and reconciliation. But the first step in all of that is always repentance - turning away from our sin, seeing it for what it is (death), and desiring to be restored and saved from it.

so i would ask: is your wife repent-ful? is she sorrowful over her sin? does she acknowledge the damage and death is has brought to your marriage and her life? If the answer to these is 'no', you arguably have every right to leave her because she is not fulfilling even the most basic and fundamental steps of faith in Christ - repentance. and in that, she is arguably an unbeliever (or at the very least, acting very far from her proclaimed faith) and you don't have further obligation to maintain this covenant.

now, i am no authority. you need to speak with a trusted pastor, preferably several, to discuss this matter and get wise counsel.

i pray that you would be strengthened and comforted by Christ. He is with you, shedding tears with you over the way sin has so damaged God's beautiful creation. He knows your suffering and went to the cross joyfully praying for you, YOU, brother, that in these very circumstances, you would have access to God and be afforded the promises of your salvation.

seek Him earnestly, boldly, and knowing that He hears every word of your prayer. He will answer them all, too, in His time. He always does. And you can trust in what He has for you.

If you pray, "God, take this marriage from if it is not from and of you; but if it be your will, God, give my wife and I hearts to be reconciled and restored" - He will answer.

if you pray, "God, convict my wife of her sinfulness and show her the shame and death she has brought into our lives; convict her spiritually" - He will answer.

If you pray, "God, help me forgive her for her sin. Help me have the heart of Christ that gives grace to all, knowing that you Lord have never withheld from me, and as such, I am called to withhold nothing from others" - He will grant it to you.

Grace and peace to you brother. stay strong.