OP - I'm going to throw another penny in the pot (is that a saying?!) - have you ever tried to say spend time, one on one with your DSD? Got to know her as a person, taken her out shopping etc... Because then (tell me if I'm being totally naive here) I'd imagine it would make her feel that she has a relationship with you, something tangible... and also with the other DC. But the DSD seems to be the one who needs understanding. Also don't forget if she's 13 or 15 she will be going through puberty, having hormonal changes and the last thing she wants is not to feel loved etc... by her DF but also by YOU!
My DSM (step-mum) I got to know when I was 13, with my DB. She had 3 DC (2 when I met her), one yet to be born and the eldest was 7 I think.
From the get-go I met her and developed a relationship, I bought the DC presents, visited etc, stayed overnight. But for her part she treated me as similar to her DC as she could - she invited us to live there, come on holiday, got me to confide in her (as much as I could/would etc). She was always supportive, kind and loving. When they got divorced when I was 21 a few years later things eventually went downhill (I think DSM had an affair) but when she was with my DF she made a huge effort, so did her family and we were both made to feel welcome.
I really do think like some others have said you seriously have to rethink your relationship with your SO, you cannot live with him/DC when they stay not standing the DC. OK you can maybe request the DC's behaviour is better sometimes about how they speak to you (respectfully etc) but I can see from the DC POV is all they get is their future DSM hates them and wants them our of the way. I hope you get this sorted though, good luck.