You have a really difficult situation because it appears that whatever action you decide to take, someone will be able to say, "you could have handled it differently". If I were in your situation, I know what I would like to do. However, I am going to try to advise you on what you should do.
As much as I would like to think otherwise, you are participating in a semi-cooperative, competitive environment. While each person is motivated to play well with others (literally and figuratively), each person also has consider that their "seat" is granted to them by the authority of another. Therefore, each person has to retain the "right" to be first chair based on their relationship with and the perception of their value to the leader. In your case, the president, by her actions, is clearly telling you that she does not think you have earned the right to first chair. So unless you believe she is open to reconsidering her perception of your playing ability, it is not likely that she will change her mind of her own accord.
So your next decision is whether you can live with this until a change comes. If you are certain that her perception of your skill can be changed by determination and hard work, then it may be worth sticking it out, especially if you are getting a lot of benefits out of rehearsals with your group of musicians. However, if she is dead set against you playing first chair, regardless of your skill level, then you may want to move on to greener pastures. You may be tempted to believe that staying is the right thing to do and is best course of action to preserve your "witness" but keep in mind that PEOPLE CHANGE JOBS ALL THE TIME. If you are unhappy in your place of work, do you stick it out or do you look for a better employment opportunity?
We tend to look at activities related to the church as though we have to stay in the same part of the vineyard until we are "graveyard" dead. But each week, there are thousands of fellowships that desire to have commited musicians who will play for the "love of the game." If you choose to stay in your current situation, it's because you think there is something there that is worth overcoming some adversity to achieve. However, if that is not the case, respectly resign and seek another opportunity. One of the world's largest evangelistic movements got started because its leader didn't fit in in the mission he tried to join. One day, he was told that he didn't fit. He agreed and and left to start Operation Mobilization.
