Help with cats?

My daughter’s cat lives here. She has always had other cats and dogs around her. I got myself a kitten, 8 mos old, about 2 months ago. I am at my wits’ end with the older one. She stalks the little one and beats her up. I think I’ve tried everything but maybe you have some advice. The little one learned quickly not to come in my room because the older one occassionally sleeps on my bed. They are both spayed and the older one is by no means a lovey cat. My beloved cat died about 2 years ago and I finally felt okay with having a new one.