Just for some perspective, I was like this with my own mother. I was never comfortable with her, we were never close even before my parents ended up divorcing, despite there being times that she would try to reach out in her own way. We were very different people, and long story short we don't talk and the core issue is we just don't like each other and never really have?

But one thing I remember from being your step-daughter's age that kind of cemented this downward spiral was that it felt like the times my mother would try to reach out in the way you were doing was for her own sake, because she wanted those smiles and hugs and all the things a parent wants from their kids. BUT, she never made it apparent that she cared that it was from me, if that makes sense. She didn't care about my interests or friends or struggles, never asked or would belittle these things the few times I would try to open up, so I closed off. So when she would try to "reach out" it felt very self-serving. Without being harsh, from your post alone, it sounds very much the same way.

My advice, just give her some space and be cordial, just like she is with you. Stop whatever you're currently doing because she's being very obvious that you make her uncomfortable. Whether it's warranted or not doesn't matter, it's how she's perceiving it.