Should I have "humility" and go to this party of a "fake friend" who I don't like?

If your parents are close to hers, or your families are otherwise associated with one another, it's a good idea to make an appearance. Go to the party, bring a card, congratulate her and give her a hug, then make your way back out after half an hour or so. Let her know ahead of time that you have plans that you just can't cancel, but make an appearance anyway.