I am married. My wife is not Jewish. I love her very much. When we got married one of the things that I loved about her was her faith in Hashem. 7 years ago she rejected Christianity and become a righteous gentile. When we married I was becoming more religious and with her support we now keep Shabbat, eat only Kosher and keep the Mitzvas. She would like to start a formal conversion before we have children. We were married through a civil ceremony. Once she finishes her conversion we would like to have to have a second wedding: an orthodox wedding. Is this possible since we are already married?
If her intentions are sincere and her faith in the G-d of Israel is true, it is not only possible but also recommended. Good luck