Wow, as I'm reading your letter, my immediate thought is this. Does your daughter mirror your social skills?
Seriously, (1) you believe that an adult or parent can and should demand (dare I say bully?) a child into being a friend and playing with your daughter at school. (2) Then you threaten the child with banishment from your home, and extend the banishment to her entire family.
Have you ever asked the other girls why she they don't play with your daughter at school? They may have an answer that sheds some light on the situation. Or the girls may not have a clue to why they ignore her.
After you "bawl out a little girl" there are probably a few that are scared.
Have you had any success, scaring them straight? Some of these girls are going to decide you are "a head case."
I was a kid who "did not" who click with other kids. I was "old" for my age.
At home, I was in charge a lot as the oldest of 7 kids. I read a lot, was opinionated and quick witted ( I was funny,) my clothes weren't cool nor were they dowdy, I was terrible at sports, and had a tiny desire to get better at sports. ( I was sadly uncoordinated.) My grades weren't great nor were they terrible.
I know you are frustrated, saddened, disappointed and mad as hell! The M. from last night, is more desperate than you. She decided that getting bawled out by another adult, would make more of an impression on her daughter. That M. must feel terrible, your house is the only game in town, for her daughter.
I was one of those girls who never had friends in elementary school. I had cousins who played with me at our homes. And we had so much fun! Yet, we never played or socialized in school (although, we were in the same grade.) There was a neighbor girl in my class, on the rare occasions we played together at home, we had fun. Voila the next school day, I was ignored and not invited to be with her and her friends.
In my opinion, girls tend to travel in packs. As an adult I realized, that I didn't click with other kids.
In eighth grade, I finally latched onto a group of girls. I didn't realize it at the time, but each of us were school misfits in our own way. When I started inviting my newfound friends to my parents house, my parents didn't approve. These girls were a little too loud, too wild, too much into music, danced wildly to music, laughed too loud etc... Interesting, isn't it, when I found my own friends, they didn't measure up to my parents expectations. Enough about me, that was 60's and 70's.
It's time for some 2011 ideas. Your daughter, may find her muse and may find a "real" friend through dance class, ballet, acrobatics, swimming, band, art, or through classes at the Y, or Girl Scouts.
My personal favorite is 4-H (my kids raised beef cattle from weaned calves of 300-500 lbs to 2000 lbs. and sold them at the county fair. Fear not, 4-H has more affordable projects such as sewing, knitting, raising vegetables and on and on. The upside to 4-H is the friends she could make in a 4-H group.
In the year 2011 there are so many options, choir, church youth groups, soccer, tennis, softball, ice skating, skate boarding, hockey, volleyball, horses, working as a tutor, or mentoring little kids.
I think it's time to back off. Offer some outside activities to your daughter, if she wants to join any of them, stand back and let the cards fall where they may.
I wish peace in your heart and mind, for both you and your daughter.
A.