While a common misunderstanding, your first sentence is not a correct statement of the law. Adverse possession does not typically arise by virtue of a misunderstanding.
To give you your "chances if you go to court" is to try to predict the future without knowledge of the salient facts. How long has the fence been there? Who put it up? How many times has the land changed hands? And so on. I suggest you retain and/or consult with an attorney who has experience in real estate disputes, quiet title actions, and so on. Our firm does, as do many other fine firms in Iowa. Best of luck.
You can reach our offices directly at (515) 288-6041. The comments listed here are of a general nature and should not be understood to create a formal attorney-client relationship -- that is, I am not, and I cannot give you legal advice here. I am licensed in Iowa and to become your attorney, I need to understand the particular facts and circumstances of your legal question.