Nah she doesnt. Edward described it several times, her power [which is nothing supernatural] is her 사랑 for the family. Plus if 당신 check the vampire index on the back of Breaking Dawn, 당신 will see she is not marked
posted over a year ago
I don't think it's solely reserved for her family though. I think it's just her ability to 사랑 anyone passionately like Edward says on Twilight page 307.