Ok, I have no idea what NT means, but it sounds like the issues you are having with this family are simply issues that are going to arise as children become more socially aware.
I have tried to really expose my children to many social situations, diverse populations, my sister's husband is African American and their children are totally normal. I'm thinking we're doing a decent job. I'm thinking my kids are aware of differences in our world. Wrong!
So we're at the store the other day and I'm chatting with the cashier and my 5 year old looks at her and says, "You have a big nose!" Horrifying. I applogized to her and immediately had a discussion with him.
A couple of weeks ago we had a cookout at our house with some family and friends and some of my co-workers. Ok, I teach math at a university, so you can imagine the diversity in this group. My coworkers are from - Taiwan, Hong Kong, Vietnam, Japan - you get the idea. I was visiting with one of the families and, thank fully, did not hear my son. Apparently he and his cousin were playing with their eyes and saying, "We're Chinese!" My SIL pulled them into the house and had a talk with them (Thank God!)
I'm just so embarrassed by these events. I am horrified that I have not already done a better job of teaching him about diversity and acceptance and making fun of people. Looks like we have work to be done.
My point is, I'm not certain any of what you're talking about has anything to do with the special needs sibling. It really sounds like this mom and daughter have some work to do, as well. This falls into the category of "totally age appropriate behavior, but work to be done."
You are probably going to run into more than your fair share of this, but rather than worrying about what work the other mom has to do with her daughter, I'd focus on being very proud of your daughter and how she has handled it so far.
It's possible this girl will become even meaner. It's also possible her mother will increase her efforts to teach her better understanding and more appropriate behaviors. I actually feel sorry for the girl, because it seems like she might end up alienating people if she doesn't begin to change her attitude.
Looks like you're doing a great job so far!