I think from what we have seen and learned from DH that Petunia was bossy, but envious of her sister. She loved Lily, and wanted to be just like her. She only became rude when she couldn't be like Lily and go to Hogwarts. She was probably a very annoying little sister, following Lily around, doing what she did.What do you think Petunia was like when she was younger?
Hope this helped.