There is absolutely nothing wrong with you or your actions-you didn't go to the director and play the sympathy card - you simply asked if there was anything that you could do in order for her to participate in cheerleading, so do not feel guilty about anything. I don't think that she is going to grow up believing that she will or should always get her way because of the hardships she has suffered. She has wonderful grandparents to guide her down the right path, and and if anything, the hardships she has suffered and overcome will make her stronger.
You are a wonderful person, don't ever doubt yourself.