P.M.
This was something that happened in my family that caused a lot of bitterness and hard feelings on my end - the older sister by 10 years.
My Mom would either refuse to let me do something or force me to take my sister along. She didn't want to tell my little sister no, or make her feel like I could do things she could not. I know this isn't your original issue - but I'll help you from it becoming one.
You need to tell your 4 year old that her big sister is OLDER and can do many things that she (the 4 y/o) cannot yet do - like sleep overs. When her big sister is driving, she will still have quite a way to wait. Nip it in the bud right away about letting the little one do almost everything the older sister can... it will eventually cause hard feelings.