Lana,
The whole topic of divorce and Catholic teaching is something which seems to always bring up a lot of emotions. Don't feel bad because you are upset. Marriage (and in turn, divorce) deals with our love, our heart, betrayal, and hurt from people who made promises that weren't kept. Very importantly, it deals with reconciling with ourselves and forgiving ourselves for our part in the hurt too. During this time of intensity, it is often difficult to come humbly before God in prayer. ... As you said perfectly, it is a complicated subject. There are many layers involved in this process. ...
I am not a Canon Lawyer, so I can only respond partially to your specific question. A trained tribunal priest would be the one to ask for a more complete explanation of the elements listed in your scenario. However, I can share with you what I know and understand because I have learned about it in my time as a Catechetical Administrator and, I can provide some firsthand insight because I went through the annulment process myself. So, please allow me to share some of my experiences and maybe guide you to others who can provide more!
Some of the reasons for the annulment process is to help the Catholic stay connected to the Church, to protect divorced Catholic from making same mistakes in other, future marriages, and to help the people involved with the failed marriage to heal.
We Catholics accept marriages from other Christian denominations as valid, so I don't see that the person in your scenario could pretend that the marriage to the non-Catholic Christian never happened. Even though there was not a priest present, a Christian marriage occurred. We Catholics also believe that once Catholic, always Catholic - ie; when one would leave the faith and return later, that person would not have to go through instructions to become a Catholic again. That person would just have to go to confession. So, in your scenario, that person, even though not practicing Catholicism, would still have been Catholic when he/she got married but would have been married outside the auspices of the Church. Should she/he have stayed married to that non-Catholic Christian and returned to practicing the Faith, she/he would have been asked to have the marriage 'validated' - which is a special type of ceremony which blesses the union.
My guess is that in the case you present, the person who married the non-Catholic Christian would not have had a 'validated' marriage, but a determination of its status would require some research by the Canon and Tribunal Lawyers. They have the details of the Church regulations regarding what the Church sees as Christ's mandate to us for marriage. It would be a sort of annulment process, however, I don't think it would be long and drawn out.
On a personal note, the annulment process was very healing for me - and although at times I resented that they were "telling me what I could or couldn't do," I discovered that I had a bad pattern in some of my decision making. By bringing this to my attention I was able to get some counseling and re-train my thinking so that I didn't follow the same bad pattern in the future. It truly helped me become a better person: it drew me closer to God, and allowed me to choose a man I would never have dreamed possible for me. We have a wonderful marriage and are just entering our 8th year of bliss!
I would guess that the healing and awareness I experienced is what the Church also desires for that re-turned Catholic. If the scenario you presented is a real case about someone you know and care for, you could call the Office for the Tribunal in Pittsburgh 412-456-3033 and ask them for guidance. Their email is tribunal@diopitt.org
For more information, you can also look on the Diocese of Pittsburgh's website at diopitt.org and type in Office for the Tribunal.
More information on what Catholics believe about the Sacrament of Matrimony can also be found in the Catechism of the Catholic Faith paragraphs 1601 -1666.
Oh, and one more thing ... this is very timely ... As recently as the last couple of months, our bishop of the Pittsburgh Diocese, Bishop David Zubik, in response to the request of Pope Francis to the Bishops of the world to do what they could to make it easier for divorced Catholics to more fully participate in the Faith, has waived all fees to the partners involved in current and future annulment proceedings! It is a process involving many mailings, copies, hours of scrutiny etc ... (just like any court case) and the Bishop is paying the fees from the parish share monies! What a generous offer to those who may not have the resources to follow what the Faith asks of her children!
I hope this helped. Thanks for your thoughtful question.