These are several wild assumptions without evidence. OTOH, it is a matter of public record that she was divorced and living with another man without benefit of marriage.
I don't know if it's up to each diocese or what, or whether you are reading very old Canon law (the Council of Trent that you cite is 16th century, and there have been a multitude of changes since then, like it or not).
The citation is a matter of Catholic Dogma. It is part of the faith, and is perfectly clear in the Gospels.
And He said to them, "Whoever divorces his wife and marries another woman commits adultery against her; and if she herself divorces her husband and marries another man, she is committing adultery." (St. Mark 10.11-12)
The grounds basically are described as that there was no "real" marriage in the first place, and it has been variously defined according to each case.
Adultery is not one of the grounds.
Adultery is not one of the grounds in and of itself, but it could be extrapolated from the adultery, and by working backward, that it represents the invalidity of the marriage. That is the rationale that nullified my own parents' marriage, so I do know it does happen in some dioceses.