What course of action would be implemented by the Cheif Executive Auditor (CAE) if Management insists on not implementing the corrective action?

Report to those charge with governance.

If there is no logical and legal justification for not implementing the corrective actions, a report need to be prepared and submitted to the Board of Directors, and a copy to the department' or unit' direct director

First of all CAE is not responsible for implementing the corrective action, it is the management responsibility, If management refuse to take any action on recommendations given the IA, he should discuss with the management to know the reasons for their refusal and if still auditor is not satisfied with the management response, assess its impact on future operations of the company, and re-assess the management integrity and communicate the matter to the Board.

Chief Audit Executive must check the reasons of not implementing the corrective actions.
If corrective actions are necessary and management insisting on not to implement then CAE should address the issue to Audit Committee and in some circumstances to Board of Directors.