When request for a long holidays then you only need to apply it to your direct person who you are reporting to. Like your case, you ask the approval by me which is correct. But you do not need to copy to others. I saw your copy mail and those people are not the person who you report to so no need to copy your mail.
But if you would like to have your colleague to know that you will not be in the office during which period the it is good to share with them after got my approval.
Any question , clarify with me.
And I hope all the copy person related to this mail also understand the procedure.