I really feel for you.
You sound like a genuinely caring yet burned out, stressed out, frazzled sm who has put up a bit of a protective wall around your family because you're just at the end of your tether. I really feel for how hard this must have been for you - must still be for you, and even more so now you are pregnant again.
In the context of your history together as a family, it is totally understandable that you feel worn out, that there's no other solution than to detach and just emotionally disinvest in this little girl... and yet, I think what's happening a little is that you're a bit stuck in the story of who she "is" (again, very understandable in the situation).
The difficulty with this, and I say this as gently as possible, is that our minds evolved generally to want desperately to avoid difficult emotional experiences - to run, to hide, to fight - but this tends to be a counterproductive, suffering-producing strategy in the long-term. It tends.. as awful as it is.. to make things worse.
So though every part of you may be screaming against it, the paradox is that your best bet is to do what's counterintuitive and lean into this, open up, be present and do what matters... because when a child becomes the "scapegoat" in a wider family situation, that has the potential to impact seriously on what the rest of the children in the home learn about love.
They learn that if you do behave a certain way in distress, you may lose not only approval and support, but also love... and so, I'm wondering if you could see the need to behave lovingly towards this little girl as being in the service of your values for your ds and your unborn child, rather than necessarily for the benefit of your SD1?
And really to dig deep into what is most loving here.. and I actually think that not making her needs the centre of everything and limit and boundary setting may be part of that. I also think that things like taking time for self-care and doing what others have suggested - not setting yourselves up for a fall by planning nice things on the weekends she visits - might be important too. And then, in so far as you are able to in the context of your life at this time, trying to bring an attitude of playful, accepting, curious empathy to her. Even if, for now, the only way you can do this is in your imagination when she's not there - or imagining her as someone else's stepchild. Just trying to get a flavour for what it's like to be her, taking a step back from all the pain and hurt of it?
That may or may not be possible for you, but for your own sake and that of your children, I would work to try not to close my heart to a little girl in distress - even if you can't spend much time with her. That will take a large toll on you. I'm sorry you are going through this.