1. Cultivate a climate of honesty and professionalism in a 360 degree radius around you. That means that you have to take action in the following ways, and perhaps in others as well.
2. When the admin seems to undercut you, meet with the person involved - not with the person's boss. Explain your perspective and ask if that is what was intended. Let them explain the offending actions and ask questions about things you don't understand or with which you disagree. Ask for what you need for the situation to be different.
3. Meet with all of your assistants and explain the importance of teamwork and mutual support - including the importance of team members representing each other positively to students, parents, admin, etc. (Matters of a negative nature should be handled one-on-one or within the confines of a staff meeting.) After that conversation, address the issue again the first time the behaviour continues - but one-on-one with the individual assistant whom you believe is still involved in not supporting the team.
As head director, you must realize that someone believes you are capable of handling the daily activities and the PR involved in building and maintaining a program. Learn to believe that about yourself and take action to make your environment what you need it to be. That is part of the job, and no one will do it for you.