My step daughter doesn't like me.
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So, my step daughter (LR) is 12, and apart from the fact that she watched her parents split then watched me come into her father's life, I'm only 9 years older than her. Maybe this is the problem? I try to reach out to her as a friend and sometimes that works, we get on great if it's just us but as soon as her dad comes home or if her little brother (who's I have a great relationship with) is with us she changes and I don't understand it.
I'm wondering if anyone else has had a same experience?
The small difference in your
The small difference in your ages might definitely have something to do with it.
My suggestion would be to give her her own space. Don't try to make conversation with her or spend any time with her unless she initiates it with you. It might take years for her to do that. She may never do that. That is ok.
I do think her dad needs to insist that she be civil to you. When I was 13, I had a student teacher who was 21. It was interesting because up until then, my teachers had been much older than me. Some of my classmates took advantage of her closeness in age to us and gave her a hard time. Still though, my parents told me I had to treat her with the same respect I showed my other teachers. I think that's the way her dad needs to look at it. She might have, or will have, adults in positions of authority in her life (like teachers, coaches, etc.) who are close in age to her whom she'll have to treat with respect even if she doesn't like them. She should behave towards you with the same civility she'd show towards them.
Also, what's happened in her life? Maybe she'd benefit from counseling.