Confide in your deputy that you think she has the potential to move toward a headship of her own. Give her a couple of days to let that sink in and then send her on a course. Butter her up a bit. Groom her for headship elsewhere. In an ideal world you wouldn't need to do this but desperate times call for desperate measures. If the first part of this plan succeeds you will then be looking for a new deputy head. You will be amazed at how cordial your staff then become.