I only have 1 child, a 15 yr old VERY strong willed child. My Ob made a comment the day she was born about her being strong willed. She's been that way from day 1.
Please, don't squash this personality trait of her and don't punish her for it. YES, it is very hard at times but in the long run, you may end up with a leader and you will have a child who will stand up for herself.
I am not a believer in spanking and we never did that. Our time outs were taking her favorite things and putting them in time out.
When our daughter was 7 she expressed an interest in martial arts and we went with it. The first school was more of a belt factory (pay your fee, get a belt, etc). We went with a private school, much tougher and she earned her black belt. She learned how to use her strong willed personality in a positive manner. She learned perserverance, respect, etc.
She is now 15, captain of her high school cheer squad, much loved and respected by teachers, very much a leader, and accomplished at playing the violin.
I agree, it is hard but find a way to balance this and direct her personality in a more positive manner. You will be happy in the long run that you don't squash her personality. Many parents choose to do that vs embrace a strong willed child.
I know without a doubt that my child will stand up for herself, defend herself if needed and speak up when she needs to.
Best wishes.