I had a similar situation with DD in nursery when she was 3. She was forever coming home saying Matthew did such and such - shouting, hitting etc. So in the end I went to nursery and said "so what's the deal with this kid Matthew?". They said he was non-verbal and suspected autistic and that he got very frustrated and tended to lash out or yell at the kids sometimes.
The approach that I took with DD was to point out that she could chatter away with her friends at nursery and join in and sing the songs and so on. Then I got her to think how Matthew must feel when he couldn't join in and couldn't get people to understand him. She thought for a while and said "I think I'd be sad and a bit angry". It helped her to see that Matthew was finding it hard to deal with being the odd one out in a (quote-unquote) normal group of children.
She came bouncing out of nursery the following day and announced "I was Matthew's friend today, mummy".
I wouldn't say things were totally perfect after that, but they were certainly better. DD has always been an empathetic child and able to relate to others' feelings, so that helped, but it might be an approach worth considering.
This story brought tears to my eyes. Thank you for teaching your child such a loving response. As the mom of a non-verbal, very autistic mentally handicapped young man I can tell you, reactions such as your daughter had do no happen often enough. It is so much more common for our kids to be ostracized simply for their differentness.
My son, Christian, a the "look" of his particular syndrome. It's very rare and you probably woudn't recognize it, but you would know the instant you meet him that something is wrong. He's a sweet, darling boy with NO behavior problems*he's been easier to raise than my "normal" 23yo ever was!* When Christian was 3yo he entered the local Special Needs public school preschool. I was very nervous about it, but kept an open mind. About 2 weeks later i was taken aside by two other mothers who proceeded to tell me that my son was "bringing down the collective IQ and functionality of the entire class." Huh? To put a fine point on it, they wanted me to remove him from "their" class so their kids "could get a better education." They felt that somehow Christian was taking up too much time from the teacher. Ummm, ok.I thought this was a preschool that my tax dollars had funded for the education of kids with all kinds of special needs. My bad.
It was a devastating experience. I did NOT remove Christian from that class, however I did talk to the teacher and she was horrified by the apparent "classism" going on--one paren'ts child has Down Syndrome, the other has severe CP but is brilliant. I guess Down sydrome and CP out-trump all the syndromes nobody ever heard of.

the teacher reassured me that Christian was NOT taking over classroom resources, and in fact, they had been able to acquire an extra parapro just because of his presence.
The interesting twist to this story is this: Despite the fact that these to mothers were so hateful, their children were not. The boy with CP called Christian "my friend" in a public place and his mother nearly stroked! She was so embarrassed! but her son remained steadfastly Christian's friend. The girl with Down Syndrome swims with Christian in Special Olympics, and while she is definitely more functional than he is, it doesn't seem to make a bit of difference in their friendship. Both of these kids have remained Christian's friends for the past 12 years despite their parents' idiocy.