Welcome, Jenn.
First, I hope you have not used real names anywhere, for your own security (and your children's) you need aliases. Also, if you use real names and at any time need to vent, your words (say, a whine about the school or a teacher or a doctor) could be tracked and used against you. I speak from experience. If you have done this and want to change it, let a moderator know and they will help you make the appropriate change.
To help your g understand, I suggest you get from the library and read together, "The Curious Incident of the Dog in the Night-Time" by Mark Haddon. It is a work of fiction but written from the perspective of a teenage boy with Asperger's Syndrome (in Britain). The character (Christopher) is obviously very bright, but also has a lot of difficulty especially dealing with people and anything that really challenged him. His life is ruled by his need to have everything the way he wants it and can understand it, but life throws him some challenges and changes so he has to use his brain to find a way through. It is not pretty - you read it first to see if she can handle it. But it is brilliant in how it not only depicts what life is really like for someone like this, but also the deeper story that Christopher still doesn't 'get' but which the author successfully tells through Christopher's observations.
You've listed Asperger's as a possibility with your son; that also increases the chances tat your older daughter could have some Aspie traits. And speaking from experience with my own "Aspie-lite" daughter, girls are harder to pinpoint with this, because they often don't show the same sort of problems. When easy child 2/difficult child 2 was 8 we had no idea she had any problems at all, she was our genius child who actually scored brilliantly across the board, including the various formal tests of social skills. But other problems began to show up soon after age 8. The first big problem we had with her was arrogance. Interestingly, we had similar problems with both boys. Next problem (all three of them but especially the younger two) was a sense of "I am equal to everybody else, there is no distinction between adults and children." Imagine a small child, hands on hips, getting angry with me saying, "I told you I wanted JUICE and you gave me water! Don't you ever listen?"
She was dishing back to me, what she learned from my behaviour toward her.
And that is a classic Aspie thing. They give back to others the same treatment they have received from those people. So a teacher using sarcasm will find the child being sarcastic to them.
I'll put my thinking cap on about any other ideas, but another possibility is anything you can grab in the social story range, even if you have to write them. I remember a lady at church donated a stack of books in the range, "Let's talk About..." and there were topics like "Let's talk About stealing", "Let's Talk About Honesty" and so on. They worked very much like social stories and taught our kids a lot that they simply couldn't learn as well any other way.
Also, you may need to teach her compassion by demonstrating it yourself. Show her how to be compassionate to this child. Maybe she could read a book to this child. But I remember difficult child 3 not understanding that a 6 month old baby could not interact with his reading a "Spot" book to him (the baby). difficult child 3 was trying to get feedback from the baby "Where do you think Spot is hiding?" while the baby was just enjoying the impression of someone talking to him and paying him attention. We were in a doctor's waiting room, the scene entranced everybody, but they didn't know about difficult child 3's autism.
We finally got through to difficult child 3 with a social story. We wrote down for him, "You are very clever at some things, they are easy for you. Other children don't find those things so easy. But other children do find other things really easy, and for you they are difficult. Other children play games together and seem to understand the rules even though you don't remember hearing them explain the rules in detail. They just read the information form one another somehow. This feels unfair to you, but to the other children, they don't understand why you find it difficult. It doesn't mean they're clever and you're not; just as your being good at maths doesn't mean you're smarter than they are.
It's just different.
We're all different. That's OK. The world would be a boring place if everyone was the same.
So we help one another. You can help a child who is having difficulty with something you find easy. In return, if you are helpful and kind to others, they may help you with things you have difficulty with.
It is important to have compassion. It is easy to lose compassion, especially when you think you are brilliant at everything. But a person who thinks they are brilliant at everything is already unaware of one thing they need to learn. It is humility. And it is very important. If you want people to love you, you need to learn to love people, even those who don't seem very lovable.
We are all lovable, there is always something about every person that is wonderful and special. Find that something and you will find you enjoy being with that person more than you thought you could."
See how that works (or something similar).
Marg