And this is where a lot of us in this situation question the process. The word “adulterer” is equal, whether or not your spouse filed for divorce, cheated on you, left you, even if you fought to keep the marriage alive, or if you cheated, lied, became promiscuous, broke promises, etc.
I think the two above individuals are very different, yet we are tossing them into the same “adulterer” bucket. This is very concerning. Certainly, in both cases, a lot of time, healing, retrospective, examination of conscience, and change of behavior is needed - but in different degrees entirely.
The two individuals are in different situations. Your first situation may be a person who has committed sin, whether the current (first) marriage is valid or not.
Filing for divorce is not in and of itself sinful. And in any number of circumstances, the one “fighting” to keep the marriage together may be the one causing the other to file for divorce.
“Cheating” is a sin whether or not the marriage is valid. If the marriage is invalid, then it is the sin of fornication; if the marriage is valid, then it is the sin of adultery. In either case, the individual doing so is most likely causing damage to the other in the marriage, validity or not.
But neither of these matters are grounds for a decree of nullity; that is granted only for an impediment that existed on the day of marriage.
If a couple is in a valid marriage - that is, there is no impediment existing on the day of marriage - and one of them gets the “7 year itch”, commits adultery, and one or the other of the marriage files for divorce, neither of them are going to be able to marry again in the eyes of the Church. They will not receive a decree of nullity.
Which brings us around to the marriage vows - “until death do us part”. The Church does not refuse communion to a couple who divorces; it refuses Communion to a couple who contract a second marriage when one (or both) were in a prior marriage, divorced, and no tribunal has issued a decree of nullity.
The point is, one is not an “adulterer” if one is divorced; but one becomes an adulterer when one chooses, after being married and divorced, to marry again without having a determination by the Church that one’s first marriage was not valid. It really does not revolve around the grounds of the first divorce. That could have been because one wanted children and the other didn’t; because of “cheating”, because of violence; because of a mental breakdown or mental disease; or simply because they became bored with each other (often referred to as an “amicable divorce”). None of those issues make the first marriage invalid.