I'm upset that my family won't let me hold my sister's new baby.
How could they? Why would your family keep you from holding your sister's new baby?
I tend to be accident prone and klutzy.
Your family is just trying to protect the new baby as you aren't responsible enough to handle him properly. So, being upset with them over this is misplaced. Learn how to pay attention and control your actions so that you can one day be able to handle him properly.
I'm very responsible and a good caretaker. My family just doesn't like me.
I understand that you might feel that way, but I'm sure they love you very much! They just want the best for the child. How about still visiting them, and admiring from afar?