Couples separating and remarrying, who is to Blame?

Firstly, I don't know the other situation why they did separate. In the Bible, Christ has a provision for someone separated from his spouse to marry again.

The depends on the situation.

For example, your wife committed adultery and left you, you can marry again. You will not sin grievously. But, for example, she did not commit adultery, you are the one who left her and married another that is really a sin against God.

Let us read at Matthew 19:9,

19. And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.

What the Lord Jesus said is clear, "Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery:" He said, "... except it be for fornication," if you put away your wife because she committed fornication, and you married another, you will not commit adultery because she is the one at fault.

She was the first. You were aggrieved by her because she committed fornification.

You can put her away and marry another. You will not commit adultery. But, for example, your wife did not commit adultery, she did not fornicate, you are the one who fornicated, you really are sinning then.

Now, what I can tell is "a sin committed by a man outside the truth, if you do not know the truth yet, that can be forgiven by God."

Mary Magdalene was a sinner, but when she obeyed Christ, all her sins were forgiven. The same with the Samaritan woman who had six husbands, but she was forgiven when she obeyed our Lord Jesus.