I begin with The Word of Grace and Truth:
John 1:17 For the Law was given through Moses, but grace and truth came through Jesus Christ.
John 1:14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
Q. "If a person is divorced and remarried, are they living in a perpetually adulterous relationship?"
A. NO!
A lawfully(i.e. God's Law)divorced person has no wife/husband. Such persons are not married.
Therefore,if they marry they have not sinned nor are they living in a perpetually adulterous relationship.
Rome may say to the contrary, but we are not romans who follow the Pope and her abominations taught by her. We are christians who follow Christ and are taught of God.
"I had a lady from my church call me a couple of years ago and tell me that I must repent of the sin of adultery by leaving my husband and remaining unmarried."
This lady from your church needs to repent for telling you to leave your husband.
When legalistic emphasis is placed on the divorce law at the expense of showing mercy to the divorced, then we find ourselves in the same legalism Jesus repeatedly condemned in the Pharisees. The person should be preeminent in the consideration, not simply a prescription about divorce and remarriage.
All divorces are merely the ultimate result which is due to man's sin. God hates the sins which lead to divorce as it reveals the corruption of the heart of man just as God hates the sins of the corrupt heart which leads a man to love money, but He does not hate money itself, as it has no sinfulness inherent of itself (a study of the original Greek language used in Malachi 2:16 and the context of the same would reveal something very different from what has been taught from this text).
The truth is that the divorce law was/is a display of God's mercy because of the hardness of men's hearts.
Marriage was made for man not man for marriage.
I know a man who asked Zac Poonen that same question(above)you've asked and below is the reply Zac Poonen gave.
(I am including this from Zac Poonen,not because I agree with everything that he says in this because some of what he says here I do not agree with,but because many will be surprised at his reply).
"We don't have any case of divorced couples in our church in 27 years - not even one. We just don't have to deal with such situations in India. This is one of the blessings of being in a poor country.
God accepts certain things in this world that are the result of man's sinful actions, even though God does not endorse them Himself. Divorce is one such thing. Each case of divorce must be dealt with individually but where children are involved, God permits some things, because the alternative would involve a lot of suffering for the children.
I don't believe you are living in adultery, because when your wife was was divorced by her first husband, neither of them were believers. So she was not under grace or the new covenant (that is under Jesus' teaching).
All those who have not come under the new covenant are under the old covenant - under which divorce was permitted (Deut. 24:1-5; Matt.19:8).
Stay with your wife and bring up the children in the fear of God. Now that you are saved, you have to think of your children and you cannot make them suffer (by you both separating from each other) because of the past history that either of you may have. Put the past behind you under the blood of Jesus and press on in to the future without any sense of condemnation.
God has a plan for your life. May you both fulfil it."
The Lord bless you.
Zac Poonen
I end with The Word of Grace and Truth and Love:
2 John 1:3 Grace, mercy, peace will be with you from God the Father and from the Lord Jesus Christ, the Son of the Father, in truth and love.