Praise be to Allah.
It is permissible to marry a woman of the people of the Book on condition that she is chaste. Perhaps this is what you mean when you say that she is orthodox. Allah, may He be exalted, says (interpretation of the meaning):
“Made lawful to you this day are AtTayyibat (all kinds of Halal (lawful) foods, which Allah has made lawful (meat of slaughtered eatable animals, etc., milk products, fats, vegetables and fruits, etc.). The food (slaughtered cattle, eatable animals, etc.) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time, when you have given their due Mahr (bridal money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girl-friends. And whosoever disbelieves in the Oneness of Allah and in all the other Articles of Faith (i.e. His (Allah’s), Angels, His Holy Books, His Messengers, the Day of Resurrection and AlQadar (Divine Preordainments)), then fruitless is his work, and in the Hereafter he will be among the losers”
But marriage to a Muslim woman is preferable.
Shaykh Ibn Baaz (may Allah have mercy on him) said:
If the Jewish or Christian woman is known to be chaste and to avoid that which leads to shameful deeds, then (marriage to her) is permissible, because Allah has allowed that and has made it permissible for us to marry their women and eat their food.
But nowadays there is the fear of much evil for those who marry them, because they may call him to their religion, and that may lead to his children becoming Christian. So the danger is great, and it is more prudent for the believer not to marry a woman of the people of the Book, because there is no guarantee that she will not fall into shameful deeds, or attribute to him children who are not his… But if he needs to do that, then there is nothing wrong with it, so that he may protect his chastity and lower his gaze thereby. He should try hard to call her to Islam, and beware of her evil, lest she drag him or the children towards disbelief.
End quote from Fataawa Islamiyyah (3/172)
It is not permissible to do the marriage in the church, because of the great evil that is involved in that, namely approval of the ascription of partners to Allah, may He be exalted, in the words that they repeat when performing the marriage ceremony.
If this woman was previously married to a Muslim man, then it is not permissible for you to marry her, until her marriage with the first husband is ended by means of divorce, annulment or the like.
This first marriage is either valid, according to what we believe in our religion, or it is an invalid marriage.
If it was a valid marriage, then the matter is clear: it is not permissible for any man to marry a woman who is married to someone else, even if she is from the people of the Book and the husband is a Muslim.
Indeed, even if she is one of the people of the Book and her husband is also one of the people of the Book, it is not permissible for a Muslim to marry her when she is still married to the first husband.
In fact it is not permissible for a Muslim to turn a woman against her husband, whether she is a Muslim or one of the people of the Book, because the Messenger of Allah (blessings and peace of Allah be upon him) said: “He is not one of us who turns a woman against her husband or a slave against his master.” Narrated by Abu Dawood (2175); classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Shaykh ‘Abd al-‘Azeem Abaadi (may Allah have mercy on him) said:
“who turns a woman against her husband” that is, he mentions the bad qualities of the husband in front of his wife, or he mentions the good qualities of some other man in front of her.
End quote from ‘Awn al-Ma‘bood (6/159).
If we assume that the first marriage was an invalid marriage, then she still does not have the right to leave that marriage or enter into another marriage, until the first marriage is ended either by divorce from the husband or annulment of the marriage by a Muslim judge. Legal divorce is not sufficient in this case, and she does not become permissible for you or anyone else thereby.
When they entered into that invalid marriage, they believed it to be valid, so they do not have the right to leave that marriage or cancel it except by the same means as they would leave a valid marriage, especially since all this time has passed. Was this marriage permissible for her in the past, when she was with her husband, then when she decided to marry you, it became unlawful, or as if it was nothing?!
In fact her asking the priest, after all this time had passed, and telling you about that, is a kind of messing about and following whims and desires for the sake of her desire to end the first marriage and enter into a new marriage, simply because she wants to!
Ibn Qudaamah (may Allah have mercy on him) said: If a woman enters into an invalid marriage, it is not permissible for her to marry anyone other than the one who married her, until he divorces her or the marriage is annulled. If he refuses to divorce her, the judge may annul her marriage. This was stated by Ahmad.
End quote from al-Mughni (7/342).
Shaykh Ibn Baaz (may Allah have mercy on him) said: The marriage is invalid according to the more correct of the two scholarly opinions, but she does not have the right to remarry until after he divorces her or her marriage to him is annulled by the Muslim judge, so as to avoid going against the view of those scholars who said that the marriage is valid.
End quote from Majmoo‘ Fataawa Ibn Baaz (20/411).
The view of the priest is of no relevance, because perhaps he thought that the marriage would not be valid unless it was done in the church.
Moreover, here we are speaking about the validity of the marriage according to our religion and its teachings. This is what is obligatory for you, and in our view what the priest has to say is irrelevant and has no consequences at all.
The woman’s saying that you have no right to ask about her first marriage is not right. Rather it is not permissible for you to marry her until you know what happened regarding the first marriage and whether she is unmarried at present.
To sum up: this woman is either married in a valid marriage, in which case it is not permissible for you to turn her against her husband, let alone propose to her and marry her;
or she is married in an invalid marriage, so she needs a divorce from her husband in order to be able to marry someone else.
And Allah knows best.