Are you freakin' crazy? Blood is thicker than water, and I would MUCH rather spend my time with my sisters (who are also my best friends) than a whiny, clingy, possessive, jealous boyfriend.
A healthy sibling relationship is the best gift a person can have. They will always have your back, love you when you are cranky, make you laugh when you are depressed, and assuming normal lifespans, their relationship with you will last longer than any other relationship a person can form during a lifetime.
You'd better learn to like her family if you want to keep her, because trust me, while she may try to meet your needs for now, your petty demands will eventually get on her nerves. This is HER birthday, not yours.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?