You are the head director. It's your vision and goals for the program that matter. Make sure your assistant understands this. If not, it may be time for this person to look for another position. As an assistant, I feel it's my job to learn how the head director wants the program to run, and then do whatever I can to help make it successful.

I do think an assistant should be able to speak privately and respectfully to the head director about questions or concerns. However, when the head director makes a decision, it's the assistant job to be "on board" with it, regardless of how he/she may personally feel.