Hello, Max. I do not know which relative you are referring to by 'cousin sister'-- we do not use that form in English. Also, may I suggest that, in my culture at least, 3 weeks is far too long to request for a wedding!
Dear Mr/Ms (Supervisor's surname):
I would like to request leave to attend my cousin sister's marriage at our home town. I would be very grateful if you would permit me to take leave from the 28th of October to the 20th of November.
Thank you.
Sincerely yours,
Max