Hi Prachi,
This situation is not a tough situation at all. I don't know whether the issue has got resolved or not, but thinking that it has not, I am providing a solution. This case, according to Organizational Behavior, is known as conflict and ego management. If you take it as a case study, you will find that the person here (at the director level) does not understand the criticality of the situation from the point of view of a director but takes it from the point of view of a lover or husband. So, according to OB, it is ego and conflict management. What you can do here is implement the DMAIC theory and plan a brainstorming session. If it sounds vague, then simply ask everyone in the company to contribute. After collecting the amount, gift her something amazing, showing the director (that person) that she has received all this as an honor of being the wife of a Director. This can be a motivating factor for others because if she gets a gift, the director surely would throw a party.
I don't know what else to say, but from a revenue point of view, losing an efficient worker just for this small cause does not prove effective management. This is conflict management and nothing else.
Regards,
Sumit Roy