I have just recently recently married a beautiful godly woman who totally fills my heart with love every day that we share together in holy matrimony. But recently we have found out that she is still married to another. Several years ago my wife was to be wed to another man but found out some rather unsavory aspects of her future husband's life prior to the ceremony. She proceeded with the ceremony but after the ceremony asked that the marriage be dissolved. Seven years have elapsed, and she has had no contact with this man and was under the impression that the marriage was dissolved. We have just recently found out that the certificate of marriage was filed and now she has to go through with an actual divorce filing to right this wrong. My question is, am I living in adultery by being married to this woman and how do I correct this situation and preserve my marriage and be right in the eyes of the Lord?
You can't have all combinations. The woman you married is married to someone else. So, yes, you are committing adultery with her.
Think about the foolishness of her statements: She discovered something bad about her fiance, but marries him anyway. She only demanded a dissolution after she finished the ceremony. Thus she freely chose to bind herself to someone she did not respect. Though she wanted the marriage dissolved, she made no effort toward that end. That too was not a wise move on her part. She then goes on to marry another man, not telling him of her former marriage.
Let us assume that her marriage was ended as she wanted. She still had no right to another marriage because it did not end because of fornication on her husband's part. "And I say to you, whoever divorces his wife, except for immorality, and marries another woman commits adultery" (Matthew 19:9).
She made a lot of poor choices in life. Her obligation under her marriage covenant remains until her first husband dies. "For the woman who has a husband is bound by the law to her husband as long as he lives. But if the husband dies, she is released from the law of her husband. So then if, while her husband lives, she marries another man, she will be called an adulteress; but if her husband dies, she is free from that law, so that she is no adulteress, though she has married another man" (Romans 7:2-3).
From what you have told me, the only choice is to end the adultery. Since you married under false pretenses, you are free to marry someone who does have the right to marry.