I would simply RSVP as no and leave it at that.

If the birthday child is sometimes a bit unpleasant then maybe it is better if your child does not go.

At the end of the day just be very clear with your daughter that once you have said no, then she cannot change her mind if she wants to go as numbers will have already been agreed with the girs parents.

Kids are up and down with their freindships like yoyo's, so probably next week your daughter will be okay with her. Just really check and double check that she is sure she does not want to go and that she knows she cannot change her mind once you have let the girls parents know. You don't want her getting upset if all her friends are going and she changes her mind at the last minute and of course you have already declined the invite and so then she can't all of a sudden say she's going!