S/D[16] has decided she doesn't want to be around me anymore

My DH and I have been married for 10 years and have two kids of our own. When we married his daughter [Casey] was 6. I'm not the proudest of how we met because he was still married and we had an affair. It was a fraught time and to her credit BM never put Casey in the middle although there was obviously no love lost between us two. Things have been chugging along at least civilly since then. Recently however, Casey has started acting coldly towards me. It's not something I can exactly complain about because she's never rude but she's definitely not friendly. She won't speak to me unless I ask her something. She doesn't just come chat with me like she used to. I pointed it out to my husband and he said that he would talk to her. Once he did he told me that she asked him if he had cheated on her mother with me. He tried to tell her that it was a complicated situation but apparently she has decided that this is enough reason to cut off any friendship with me.

I don't know how to deal with this. I know that I fucked up but that was ten years ago and I've obviously grown as a person since then. Should I approach her and tell her my side of the story? Is there any hope that our relationship can recover from this?