Regardless of the one piece of scripture in the NT regarding adultery, I'm just wondering how a believer rectifies breaking a covenant before and with God, regarding "til death do us part".
I think it is important to separate the concept of marriage with our culture on marriage.
History of the Christian Wedding
In the Old Testament, a man would pay a father a bride-price for his virgin daughter, and he would give her to him in marriage. It was the custom to have a feast. In Jewish culture, there would be a waiting period between bethrothal and marriage. Jewish culture also had marriage contracts, bridal consent, and various other practices. Some people interpret the Torah as commentary and laws written around these existing cultural practices. Another approach is to think that some of these practices evolved over time, including during the intertestamental period in Babylon.
Our 'Christian weddings' seemed to have evolved from a Roman custom of a couple to be wed standing before a pagan priest and saying certain words. The bride would say, "Where you are Gaias, I am Gaia." At some point, the man would carry the bride away while her family chased them, recreating the traditional story of how early Roman men in the early days of the city had stolen their brides away. A ring was also part of Roman marriage culture.
My guess is, the Roman Christians substituted the pagan priest for a church elder and changed the words and a few customs. That became the 'Christian wedding', and vows were exchanged. A few hundred years into Christianity, Pope Gregory, I think, made weddings the business of the church, or so I've read.
What makes a couple married
If you asked a Hebrew who'd heard Moses give the law or some early Hebrew who believed in Yahweh, he might say if the bride's father is alive, and the groom gives him a bride price, that makes it official. If she isn't virgin, he might say a father would have to give her away in marriage for her to be married.
If a woman's husband died and she had no children, his brother might have been able to marry her by saying she is his wife and sleeping with her.
The Judaism we are familiar with has certain wedding traditions. But early Judaism didn't have these men they call 'rabbis' like the religion we know of today.
What about vows?
The Bible doesn't say we get married by making vows. I suspect many of those patriarchs in the Bible were married without vows.
A lot of our wedding vows aren't 'vows' in the sense of oaths sworn in the name of the Lord. They are "Let your yea be yea, and your nay be nay' type agreements, without an oath.
I think the Roman Catholic ceremony actually makes the couple swear.
If a couple do swear an oath and don't keep it, then they break an oath. Even if there are grounds for divorce, the oath was optional. A man could swear to God that he would always give his wife a flower every morning. That would be a stupid and foolish oath. He would be an oath breaker if he didn't keep it.
If he swears that as part of his wedding vows and breaks it, his wife does not have any Biblical right to divorce her husband because he broke his wedding vows. The vows are a separate thing.
If a woman swears to God that she will never divorce her husband, and the next day he beats her to a bloody pulp, sniffs cocaine off her body, and has sex with another woman right in front of her, and she divorces him, she is still breaking her oath to God.
If a man swears to God on his wedding day that he will never divorce his bride, and it turns out she lied to him about being a virgin, and he catches her sleeping with his best man during the wedding party, then she takes out a gun, and shoots his mother, if he divorces her, he is breaking his oath.
Jesus said "Swear not at all...." If you swear and break your vow, you are breaking your vow, no matter what other people did. You don't have to make the vows. It's not even required in our culture these days, and many churches do not require an actual oath.
My main points.
1. A vow is not the basis of a marriage.
2. A spouse can break a wedding vow (especially a stupid, self-written vow) and you could still not have grounds for divorce.
3. If you believe you have Biblical grounds for divorce, that doesn't mean you aren't breaking a vow you made if you divorce.