Yes, I would stick it through the season. Why, my dad was a well known football coach in IL and he taught me to never quit. If you do, that person wanting you to give up has just won a mental battle. As hard as it is, and yes I have dealt with this, you get through it and become stronger.
I wish all parents were as willing to be supportive of your daughter as you are. Again, I do not eveny your position.