ridermom – there is no need to get her over the carrot habit. Habit is very important to horses, and carrots do her no harm, unless they become bribes. Mine get treats at specific times for specific reasons, and only one begs (he was a pickpocket when he was in training).
Anxiety under saddle can be addressed in a number of ways. With two of mine (Arabians), I vary what we do, so they never know if we are going to just WTC, work on laterals or just amble around bareback. It has helped with them. Of course, one is still afraid of the dragons, and the other is afraid of eggs and small children.
It is never the horse's fault