Thanks for taking the time to post your story. I understand your frustration and anger toward your mother. And this isn't something that just "goes away," but it does and can get better for you.
When a parent is unhappy with themselves, it's often taken out on someone else.
Although you've been hurt, understand that your mother's behavior has had nothing to do with you as a person. Learn how to not take your mother's behavior personal and you'll be able to forgive her much easier.
The same is true for your sister as well. It sounds like there may be some resentment there that also needs to be addressed.
Have you talked to your mother about how you feel? This is always recommended, but it's not needed in order to move on. Forgiving someone isn't necessarily for them, it's more for the person who is holding on to the grudge. And you can silently forgive someone without them being present.
You'll feel a tremendous burden lifted off of your shoulders when you do choose to forgive.
Get reacquainted with that little girl who felt unloved and begin loving her today..do not wait any longer!
It's time to start treating yourself the way you've always needed to be treated. Do this, and you will not need your mother's acceptance any longer.