God's ideal is always reconciliation. That is the whole ministry of the Lord Jesus: reconciliation with the Father through him. However, we do not live in an ideal world, and for this reason, God provided concessions for divorce. Not only that, but it is possible to reconcile a relationship without reconciling the marriage (I have a good relationship with my son's father, but we never repaired our marriage).
It is not your adultery which drove your wife to divorce. That may have been the final straw that broke the proverbial camel's back, but it is only a symptom of something much deeper. Why did you have an affair? There is something far deeper going on in the marriage that you are not disclosing.
I would suggest that God is no more in your corner here than he is in your wife's. She has every God-given right to divorce you, just as you have every God-given right to hope for reconciliation. I'm sure the situation breaks God's heart, but it is up to her whether she wants to reconcile the marriage.
My studies of divorce and marriage are much different than Aiki. God does not so much hate divorce as he hates sending a spouse away without the benefit of divorce (a study of language and interpretation reveals this). If God hated divorce so much, he would not have divorced Israel and pursued Judah for a time. No, God hates the state of permanent separation. He allows for divorce.
Since this is an advice forum, you might want to do a biblical study on divorce:
www.divorcehope.com.
Also pray for your wife, that God will soften her heart and she will desire true reconciliation with you as a testament to the reconciliatory power of Jesus' ministry in her own life. Pray that the Spirit draws her to himself, and that she will seek him with all her heart. And pray for your children. Also, continue to seek God yourself, whether she reconciles or not.