How Does "The Mean Girl" Make Friends?

Making friends is something we have always struggled with--well at least the last three or four years. Imma doesn't relate to other children well.  She used to try to play with the other kids but when they didn't know what she wanted or what she was trying to say, she would wander away, or they would go off and leave her.  She almost always ended up playing by herself.  This year, kindergarten hasn't been too different.  There are a few kids in her class, mostly very sweet little girls, who try to "help" her.  Sometimes they treat her like she is a baby or a little sister.  One even tried to pick her up one day.  They will even ask me how old she is.  They don't get that she is the same age they are, she just can't speak as well as they can. I tried to explain that she just doesn't understand what they are saying all of the time. One of them asked if they should say it in Spanish.  I laughed because sometimes the thought goes through my head, too.  Maybe if I just say it in another language, she'll get it!  But, no, saying it in Spanish, or French, or Chinese won't make any difference. We just have to keep saying it, slowly, with gestures, and she'll figure it out.
But five year olds are impatient and they don't always want to do that.  A lot of time she ends up swinging at recess or playing on her own.  And she's perfectly fine with that, for now.  But I am hopeful that she will eventually make some good friends and have lots of children to play with.
One day I over-heard another kindergartner, not in Imma's class, talking to a little girl next to her in the gym before school.  She said, "Oh, see that backpack over there?"  She pointed at Imma's backpack, which I had sat down while she was in the cafeteria eating breakfast.  The other little girl said, "Yay. Whose is it?"  The first little girl says, "That's the Mean Girl's backpack."  The other little girl nodded and said, "Oh, ya, the Mean Girl."  Of course, I had to enter the conversation at this point, so I said, "Whose backpack is it?
 "Oh, it's the Mean Girl's."
"Why do you call her the Mean Girl?"
" Cause she's mean to everybody."
"What did she doe that was mean?"
"I don't know.  She's just mean."
Well, I spent a few minutes explaining how it isn't fair or nice to call someone names if you don't know why you are calling them that and both of them seemed to understand what I was saying but a few days later I heard a similar conversation, this time two boys, talking about how Imma was the "Mean Girl." It just breaks my heart to know that these children are assuming because she doesn't talk to them that she's mean.  And I know from time to time Imma has done some mean things. Most kids do at the age of five.  But she's certainly not mean and she would be a great friend, if other kids would give her the chance.

My Sweet Non-Mean Girl!

We have play dates sometimes and those usually go well because I always invite family friends that she has known for a long time.  I don't know the parents of any of the children in her class well enough to set that up yet, but I think that would help. Does anyone else have suggestions of things we can do to help facilitate making friends? My girl is a very sweet girl and she deserves to know the joys of friendship just like everyone else.