First of all, I am sorry for all of the stress that this has caused you.
As far as your question, there are a few things to think about. If the "questionable" conversion is on your father's side, and your mother is Jewish, then by Orthodox, Conservative, and Reform standards you are considered Jewish. I am speaking technically here, and this does not take away from the emotional, and spiritual challenges that such a discovery might bring about for your father, his family, and your family. For that discussion, I suggest you sit down with a rabbi who you trust to help your family work through these issues. It is also important to have a good understanding of what was "wrong" about the conversion. Is it something that all rabbis would have a problem with? Only Orthodox rabbis? Only some Orthodox rabbis?
But back to your question—(1) If your mother is Jewish, you are Jewish. (2) I do not see why an Orthodox rabbi would not marry you to a Kohen. Traditionally, there were issues with a Kohen marrying a divorcee or a convert- but neither is the case here. You are Jewish because your mother was Jewish and nothing about your status should effect the status of your fiancé’s Kehunah (priesthood).
One other note: I would suggest that you and your fiancé use this as an opportunity to discuss your own feelings about your Judaism, what your Judaism means to you, what type of Judaism you want to bring into your life together. Check out some of your local synagogues, talk with your friends, meet some rabbis in your area- and then decide what feels like the best place for you to begin your Jewish life together.
Good luck and Mazal tov! I hope that all works out for you and your fiancé.