TBH, I would ignore it. There are any number of reasons she could be doing this - to incite an argument from you, she's jealous of your relationship with her dad, to keep her mom happy, to get attention, etc. As PPs have said, it's even possible that SS could be lying or trying to wind you up.
A wise person once said, "What other people think of you is none of your business". As long as SD is not being abused (which I sincerely doubt) what happens at yours is none of her mom's business, and what happens at her mom's is none of your business.
I could be wrong here, but I think you have posted before about SD's clash with you. The reality is that she is a young teen, which is a difficult age to start with, and she's now having to adjust to sharing her dad. IIRC you have been together for some time, but now you're going to formalize it in a marriage. That indicates permanency and commitment. It may not be easy for her to accept. My concern is that if you push her and punish her, she's likely to keep seeing you as the "bad guy" and you won't get any further with her.
My advice would be to just ignore it. If she says bad things about you to your face, I would respond with, "I understand that you're upset, but I don't appreciate being called that. Could you please tell me what YOU would like to see happen?" This provides you with some room to negotiate. Parenting teens is very similar to parenting toddlers - you have to let them make decisions, while providing reasonable boundaries. You also have to decide when to say something and when to let go. I would suggest this is one of the times to let go.