I assume you already have a lawyer representing you for this divorce. If so, insist they earn the money you pare paying them. When a married couple files separate returns, they are required by federal law to provide the SSN of the spouse on their return. Therefore you have a legally mandated need for her SSN and she is legally required to provide it. If she refuses to provide it, then she is in violation of the law. Let your lawyer take care of getting her SSN for you. This is one of the many things you pay him for.
