It is good you are noticing this issue and trying to find ways to address it. Imo you are right to be concerned.
My daughter is only 7, but I have already seen that she is much more peer oriented than her brothers ever were. It is tough trying to help her find perspective and learn to be true to herself, but it is a battle I am determined to fight with everything I have. I was peer oriented to a fault as a pre-teen and young teen, and trust me I am not being over dramatic when I say this tendency to go against my own best interests in increasingly desperate bids for peer approval nearly killed me.
Imo this is not entirely or even mostly about this other girl. She sounds unusually openly petty, but few kids (or adults) love it when their friends surpass them. This girl may be a particular problem, (what is she doing exactly that is making your daughter afraid to cross her?) but in the end no child can be trusted with this much influence over another kid. This is about your daughter feeling so desperate to please a peer that she is willing to deny herself her justly earned rewards in order to do so. What is more, she is willing to waste your precious time and family funds in her pursuit of approval from this other child.
I see this as a type of peer pressure to which your daughter is succumbing. If this capitulation is happening with this friend, it could happen with other friends or friend groups, a boy friend, etc.
How exactly to address this issue I cannot say. It depends in large part on what your daughter will respond to. Generally, I would suggest find specific ways to help her feel always entirely safe and protected by YOU. Keeping the parent-child bond very strong is a great way to fight peer pressure. Try to help her (re)orient herself to her family more and peers less. Maybe do more fun things as a family so her whole life feels less wrapped up with this social group. If there is time, get her invloved with something like 4H or scouting or a church group or volunteer group or something else this friend does NOT do. If there are nicer girls in the group, maybe try to encourage some one on one time with them. If these kids are socializing anywhere aside school and gym, let it be your home, where you can influence the dynamic.
Also, you do not say how old your dd is but whatever her age, I strongly suggest, keep her away from social media or keep it limited to very light and positive things ONLY with very close monitoring. Much of social media is not a healthy environment for kids or teens generally, but is particularly potentially harmful to kids who are overly concerned with pleasing others.
