When you commit a mistake and hurt someone who is very close to your heart, then you should feel it and express your apologies. You can use a sorry letter to do so as it will be an imprint of your repentance which will remain forever with the recipient.
Here is sample letter to your cousin:
14th May, 2010
I am sorry for wrecking your plans for this summer holidays. It is completely my fault and I am feeling very guilty about this. I know that I have forcefully taken the initiative to plan out the summer holidays and was trying to make the best program for the vacations. But due to my confusing attitude I was not able to make out anything.
Even you have asked to help me out for so many times but I denied because I wanted to structure the things in my way to get the experience. I was trying to be good and confident while taking the decisions and I thought it will only be possible if I will not take any help. But I was wrong as I did not have any idea of it and you had enough experience about traveling and can easily guide me, so I should ask you for the same. Just to make my planning best I spent so much of the time and now in the middle of the month I realize that it is not the thing that I can do alone.
I sincerely apologize for wasting so much of your time which was actually a treasure that comes to us once in a year. I hope you will forgive me for this and you will not have any hard feelings for me.
I am waiting for your reply.
With all my love & care,