I'm not sure I have anything else to add right now. I would say homeschool for nowm while you are looking at other options, but that would mean leaving your job and then you can't just get it back!
Would you like to appeal the decision to kick her out of that othher school? Retain a lawyer and get them to write a letter.
Does she need alot of accomodations at school? Did the private school reject her because of that, or just because they say Asperger's and didn't know how to deal with that. My son with aspergers can pass as NT at a well run school. (In a crappy chaotic school environment you can tell)

In terms of homeschooling, we don't actually hang out with other homeschoolers much. My son has neighborhood friends and so do I. We go to activities on weekend and afterschool hours. We even go to his old school for the tuesday night activities. They don't have a problem with that. It can be lonely not to have other parents round who "get" wht issues you are dealing with. Sometimes I just get blank looks, or by peoples responses i can tell that they really don't get what I'm talking about.