I guess you've got your range of answers OP. Advice is always kinda useless coz nobody but you really has the full facts
Like some of the other people, I find it kind of 'sad' that you and your DH don't love each other's kids, but I mean that literally, just sad, because my own stepdad was an important figure in my life. You can't control who you love, nobody has a right to judge you for it, and everybody's just trying to do their best based on what they know.
All that said, I think it's valuable that people have pointed out to you that your DSD is a person too and might have her own stuff going on. I don't fully understand your arrangement - do you just leave each other to talk to and deal with your respective kids? I can't see a way that that wouldn't inevitably lead to conflict and favouritism and hard feelings, side taking and alliances and politics and all that. I still don't really understand why you see it as DH's responsibility to talk to DSD when she's somebody you must have at least some kind of relationship with?
Even putting aside the commitment you take on as a parent, and the duty of care of living together/being in loco parentis, in any interaction between an adult and a child (and 12, by any measure, is a child) the adult has the responsibility to think and behave like an adult, to understand that the kid is still developing, and that this might mean picking up just a bit of the slack that you wouldn't expect to have to deal with in interactions with another adult.
I dunno, love or not, it feels like if you're not in a position to respect her enough to have just a straight conversation with her - if you're just a woman she lives with - I don't see any reason why she'd value and respect you. You can go the other way and rule through fear, lock the doors, go tit for tat, push for escalating punishment, all that, but you'll probably just be breeding resentment and storing up a bunch of conflict that doesn't need to happen. Real damage can get done that way, to the child, to your relationship, to the other kids who have to live in that environment, and because it's exhausting, to you.
And, ultimately, fighting with a kid just isn't a good look, even if you win. You're making a bit of a rod for your own back if you imbue somebody whose brain isn't going to be properly formed for another 8-10 years with the power to 'piss [you] off', and it might be best to find a way to avoid thinking about it in those terms.