When I was going through my ecclesiastical trial to retain my minister’s license, this was one of the questions being asked of me. Namely, they asked me if I had forgiven my ex-wife. Given more time and thought, I might answer that question differently than I did on that day.
I have certainly given her over to God’s judgment and have no interest in being her punisher anymore (see Romans 12:19). If that is what someone means by forgiving my ex-wife, I have forgiven her.
I am not angry or bitter towards her any more than I am bitter or angry towards a stranger with a reputation of being a moral reprobate. She is no longer my “problem,” even though I am aware that she did some really bad things.
If forgiveness means that I believe she is no longer accountable for her sins against me, then I have not forgiven her. Now, I am more than willing to offer her forgiveness and clear those accounts, so to speak, upon demonstration of her humble repentance per Jesus’ instructions (see Luke 17:3). However, I do not foresee this happening. Our last interaction–via her lawyers–indicated to me that she is far from repentance.
A more godly approach to faithful spouses regarding forgiveness is to ask whether or not the cheater has repented first.
It ought not to shock a pastor or Christian counselor if forgiveness has not been granted if the cheating spouse or ex has not repented. That sort of withholding is good and godly (see Luke 17:3).
Instead, the focus ought to be on helping the faithful spouse through the grief–including the anger–to a place where he or she can let go of the impulse to punish the cheater entrusting the cheater to God (see Romans 12:19). I see that work as a matter more about processing the grief than offering forgiveness.