I wonder if you could write on topic that deals with clash of emotions/feelings being a coward for allowing unfaithful partner back into our life without much consequences and at same time feeling like traitor to kids if choosing divorce instead.
It is not a betrayal of your children to act in a way that supports your morality and values. That includes deciding to divorce an unrepentant cheater.
It is their mother who let them down in destroying the marriage via cheating. You are simply enforcing a biblically allowed consequence–i.e. divorce–for being unfaithful (see Jeremiah 3:8, Matthew 19:9).
Also, what I hear in your question is the torment that comes when you fail to respect and obey your conscience. It seems to be telling you to divorce your cheating spouse. The Bible is clear that we need to respect our conscience and not violate them (see Romans 14).
In sum, I have two points for you to consider to get out of this soul-deadening loop:
1) Take responsibility for living out your convictions and values. If unrepentant cheating is unacceptable to you, then you need to be prepared to divorce over it. I am not talking about “punishing” a cheating wife; rather, I am talking about ensuring real repentance has taken place. To do anything less is to signal that you will tolerate such sinful, unrepentant behavior, and that teaches your children that message as well.
2) Do not take responsibility for the consequences of another’s choices and actions. Once again, I encourage you not to accept the narrative that you are to blame for this divorce. If you decide to divorce, you are doing so because your wife has refused to repent from cheating. It is not the rape victim’s fault that the rapist is in jail. He is in jail for choosing and committing a crime. The same idea here applies to divorcing a cheating spouse.
Divorce is hard. It is painful and comes with awful realities and loses. At the end of the day, you are answerable to God for your choices on these things.
Would you rather accept the loses that come with divorce and gain the opportunities that follow or continue to tolerate the contempt and sinful unrepentance of a cheater?
I think God clearly teaches us not to accept unrepentant marital infidelity. That is why He provides divorce as a option to faithful spouses (e.g. Jeremiah 3:8, Matthew 19:9). And my experience is doing the hard thing in following God brings forth blessings.
Hope that helps!