What would you do in this theoretical situation?

Problem/goal: What if the request for leave is not accepted?

Context: You are employed for 1 year+ already. Have enough leave credits. The section or department you are working in glorifies little or no rest at times. You have a family vacation abroad, there are tickets already (will use up 19 leave credits). You are already planning to resign (regardless if this vacation was or was not planned), but your family won't accept the idea of resigning without a direct replacement job right away. Vacation is in 1 month from now.

Thank you in advance, might not be able to reply to all but will read all the replies.