I'm going to suggest a different approach. Apologies for crossover with PPs.
@Cindertoffebuns, you haven't said anything that particularly indicates psychopathy (or PDA, or antisocial tendencies, as commonly diagnosed in pre-psychopathic childhood) but you have other kids with SEN and this concern only with your second child. It's fair to assume you're not anxious over this incident alone, but have observed over considerable time that DD2 lacks empathy in ways that your other girls do not.
There are lots of possible explanations for this but, yes, 'psychopathy' is one of them. Like everything else it's a spectrum - not all kids who will be diagnosed in adulthood spend their youth torturing animals and setting fires. But there's one very fascinating aspect of psychopathy that could in some ways be seen as an overlap with autism, and that you might be able to leverage to DD2's advantage.
The children who torture animals & start fires, etc, are doing it to see what happens. Once you take the compassion and concern for consequences out of it, you can see how it would be interesting. They're experimenting to find out how the world works, in much the same way as children take toys apart to see how they work. In fact, neurotypical toddlers have the same approach to other people and pets - they'll poke and pull out of curiosity, not malice. As they grow, we encourage them to think about how it feels for the other child or animal and NT kids do develop this 'theory of mind' over time. BTW, theory of mind isn't fully developed until about 25 years!!
Now pre-psychopathic kids don't have the mental wiring to do this. But they are interested in how people work and, by adulthood, most are able to correctly predict how others will feel & respond to various stimuli. They also learn how to fake the same responses, even if they aren't feeling it.
Here's my partial autism overlap: we hear plenty about how autistic people learn to 'mask' in NT society, and how to interact in ways that others perceive as friendly and/or helpful. It's the same process, by and large. Certainly close enough for a child who is still growing and figuring out how to fit in with the world.
You've been trying to teach DD2 how to put herself in others' shoes, and it's not working. She quite likely feels got at: that she's seen as inadequate because she doesn't have this range of emotions considered normal and desirable. Whether she's autistic, psychopathic or both, it's only going to leave her confused and probably resentful.
So how about presenting it in a different way? Don't ask her to 'feel' or even care about the other's feelings. Put it as interesting phenomena. Make it an intriguing set of life skills. When you throw things at people's heads, it hurts them. They cry and get upset, then they won't play with you because you hurt them. When you pinch, kick or hit other people, it hurts them. They cry, get angry and they might hurt you back. When you hurt people, adults punish you. See how that happened at X time with Y? When you felt like kicking him, what else could you have done instead, and what would've happened next?
Anyway, you know your children; you know how to approach this with her. I'm basically saying that whether she's autistic, psychopathic or both, treating this problem with detachment instead of trying to engage her emotions might well work better.
A close family member of mine has psychopathy, and I've known a few others. In some ways I quite envy it! Good luck 