Sorry. IOW = in other words. It isn’t a terribly common abbreviation, so don’t feel bad!
I think your question is this: What makes a sacrament valid? How can we tell?
Well, let’s start with the second half first. If we do our best to inform ourselves on what makes a sacrament valid and believe a sacrament to be valid in good faith, it is nothing against us if we are later proven to have been incorrect. If someone were to pass himself off as a priest when he doesn’t have the power to confect the Eucharist, yet you believe in good faith that he did, it is nothing against you that you genuflected to an unconsecrated host. You would not be guilty of failing to go to Mass on Sunday, nor guilty of giving the worship, honor, and love due to God alone to a piece of bread. It is not outside the power of the Holy Spirit to grant you the graces of a spiritual communion with Christ because of your faith and obedience and in spite of the false priest’s deception, just as if you had asked for the graces of a spiritual communion in prayer because it was impossible to go to Mass. If you made a confession you believed to be valid, you would not be held responsible for failing to confess a mortal sin because someone conned you into believing he was a priest. Likewise, a couple who believes in good faith that they are married validly do not commit fornication by having marital relations. And so on.
So, what makes a sacrament valid? There needs to be the necessary matter, form, and the intention of the minister. You are asking when coercion removes the free consent necessary for the spouses, the ministers of marriage, to enter into a sacramental covenant. Obviously, it is not necessary for the couples to have been utterly free of outside pressure to marry. That is the ideal, of course, but extenuating circumstances that change their minds about thinking marriage is the “right thing to do” does not automatically render marriage vows invalid.
**Can. 1103 **A marriage is invalid if entered into because of force or grave fear from without, even if unintentionally inflicted, so that a person is compelled to choose marriage in order to be free from it.
**Can. 1107 **Even if a marriage was entered into invalidly by reason of an impediment or a defect of form, the consent given is presumed to persist until its revocation is established.
It is possible to have two couples who seem to have been in the same circumstances, have both divorce, have both ask to have their marriages examined, and then to have one of the marriages declared valid and the other invalid. On that account, all marriages are assumed valid until invalidity is established. You don’t set fire to a building if someone might be living in it. You treat it as occupied until you are sure it is not being lived in.
The couple who have not divorced and not asked for an investigation are to be presumed validly married. We would never advise that they separate and end the common conjugal life unless the circumstances are such that we would advise a separation even though their bond is valid and they will not be free to marry anyone else.