You are giving him a way out. Why would you help him ? Company mai keyboard chle na chle dimaag chlate rehna chahiye.
Your goal: look for a job, and leave a dent on this manager.
How to do it: Extra hours should be approved by higher management and HR. He is probably bypassing them and keeping only his manager in loop and have approval off the record.( if this was on record you would already have email but assuming you dont). You want to bring it on record. He looks bad .
Ask your manager to put it in writing and mail you. Don't ask like you are challenging him . Slide it smoothly. Tell him if you get an email you will be able to show this in your performance review, and it will be helpful to you. Also, tell how he as a manager would look good that he can convince his team to fulfill extra business requirements, and this puts him in good light. Once you get that email, remove him from loop, ask his manager and manager's manager's manager if they have approved these longer hours . ( dont ask directly, improvise like you care for company and want to know how important is this) . Tell them how you well planned your holidays and staying in office would mean montery loss of tickets. ( train,plane, visitng pilgrimage, taxi ,hotels). Ask them if you could help other time.
This way the higher management, HR will know .
If they have approved it, you will get to know and they will most probably allow you to go on off.
Of they haven't approved your manager would also be looking for a job.
Remember don't give such managers a free pass. Dent them.
And look for a another job. This is definitely not the only your reason you want to leave. You must be having more, leave with style.