I have seen a growing trend among certain groups of Christians to claim that those who are divorced and remarried are living in perpetual adultery and should divorce their second spouse and return to the first spouse. This is a very dangerous and unbiblical teaching.
It's somewhat understandable that people might believe this. We live in a time and place where divorce and remarriage are frequent and even the church has largely accepted it. In reaction against the common view that marriage is easily cast aside for any and every reason, some have tried very hard to go to the opposite extreme and consider marriage completely indissoluble. Yet rather than react, we must search the scriptures to find the right view.
Here are some Bible passages that show that second marriages are legitimate marriages and that divorce from a second spouse or a return to a first spouse is not permitted.
Deuteronomy 24:1-4 "When a man hath taken a wife, and married her, and it come to pass that she find no favour in his eyes, because he hath found some uncleanness in her: then let him write her a bill of divorcement, and give it in her hand, and send her out of his house. And when she is departed out of his house, she may go and be another man's wife. And if the latter husband hate her, and write her a bill of divorcement, and giveth it in her hand, and sendeth her out of his house; or if the latter husband die, which took her to be his wife; Her former husband, which sent her away, may not take her again to be his wife, after that she is defiled; for that is abomination before the LORD: and thou shalt not cause the land to sin, which the LORD thy God giveth thee for an inheritance."
Notice that the woman's second marriage here is obviously considered a valid marriage and the scripture specifically says that she must not go back and marry her first husband again. Her second marriage was an act of adultery (according to Jesus), but it also broke the tie between her and her first husband such that it would be a sin if she ever went back to the first husband - even if her second husband were to die. That's very powerful proof that remarriage does produce a valid marriage.
Jeremiah 3:1 says much the same thing: "They say, If a man put away his wife, and she go from him, and become another man's, shall he return unto her again? shall not that land be greatly polluted? but thou hast played the harlot with many lovers; yet return again to me, saith the LORD."
Again, a second marriage makes it impossible to ever go back to the first spouse. This is clearly spelled out in scripture.
So while Scripture does intend for divorced people to reconcile with their spouse (I Cor. 7:11), that is only the case if they have not married anyone else. If a second marriage has occurred, going back to the first marriage would be a sin.
I Cor. 7:12-13 "But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away. And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him."
Notice that, in this passage, even things which would normally be a sin to do (i.e. marry an unbeliever), once they are done, should not cause a divorce. One is supposed to carry on and not divorce, but live right from this time onward.
Some point out Jesus' statement that remarriage after divorce is adultery, and that is certainly true. It is a sin to remarry after divorce. However, the question is, if someone does remarry, whether the new marriage commits adultery as a one time thing or whether the new marriage is adulterous every day for the rest of their lives, which requires a second divorce in order to stop sinning. Jesus' statement, by itself, doesn't say which it is.
Some people assume, without proof, that the second possibility is the case without considering anything else. What we should do is use scripture to clarify that uncertainty rather than make assumptions. When we do that (as I did above), we see that the Bible teaches that a second marriage breaks the ties of the first marriage and forms a valid marriage, not continuous adultery, and thus that the first interpretation of Jesus' statement is the correct one. Remarriage is a one-time act of adultery, not on-going adultery, and the correct course of action is to remain faithful to the new marriage vows.
Another thing to consider, in addition to the Biblical case I already made, is God's purpose for marriage. God intends for marriage to be a stable, loving environment for the raising of children and also a picture of the love between Christ and the church. The idea that a person must divorce a second spouse is not only opposed to clear Scripture passages, but it runs counter to the plan God has for marriage. If a person has remarried, and especially if they have children in that new marriage, divorce only causes further harm to the people in the second marriage and any children they have. It is this damage that God hates. In fact, this kind of damage is the reason divorce is so harmful in the first place. Advocating further divorce to go back to a first spouse is telling people to cause more harm that God hates.
What it comes down to is that Scripture is clear that a second marriage breaks the tie of the first and the Bible never advocates more divorce. God hates divorce. He never tells anyone to divorce. What should happen when a divorced person comes to repentance is that they carry on, in whatever marital state they are in, and do their best to live for God going forward. If they can be reconciled to their first spouse, they should do so, but if they have married again, they should stay in that marriage and be faithful.