My 8 year old son has Autism (also very high functioning), and though it hasn't been easy, I have learned to appreciate the people who get it and who appreciate him anyway and just not worry about the people who can't seem to deal with it. If it helps, I've learned that more often than not, people are accepting and understanding, even supportive!
It's not easy!!! At all! Our son has impulse control issues, and there have been times when he has gotten upset and hit or push or kicked or even bitten another child! I feel horrible when this happens. It's always been at school or at daycare or at Sunday school and usually when something has been different. He thrives on routine.
You can't make this mom understand. You can't make her be friends with you or let her kids play with your daughter. You just can't. She isn't ok with it for whatever reason, and the only way you could ever change her mind is to just live your life and hope she notices that you guys are good people and might be fun to hang out with.
It would be great if your daughter had neighbors to play with, but if it's not going to happen, it's not going to happen. Move on and find other friends for her to play with. Not every kid plays with their neighbors, and that's ok.
Of course this upsets you. I'd be hurt, too. It's ok to be hurt and upset, but for your own sake and for your daughter's sake, you have to move on.